Introduction: Only those horns that are defined as a Shofar as opposed to Keren are valid to be used for blowing Shofar. The following will discuss the definition of a Keren and which horns are thus invalid to be used.
The horn of a cow: The horn of a cow and ox [despite them being Kosher animals and containing cartilage], are invalid. If one used this horn to blow Shofar he has not fulfilled his obligation.
Horns with cartilage: The term Shofar refers specifically to hollow horns which have cartilage growing inside filling their hollow space. This negates the horns of majority of non-domestic animals of which their horn grows as a single bone without cartilage and hence their horns are not considered a Shofar. If one used such a horn he has not fulfilled his obligation just as is the law regarding one who used the horn of a cow or ox.
Example of animals with Kosher horns: The horn of a sheep, ram and goat are valid as they contain cartilage and are hence called a Shofar.
The horn of a ram: It is a Mitzvah Min Hamuvchar to blow the Shofar using the horn of a ram. If however one does not have a rams horn available he fulfills his obligation with the other Kosher horns [mentioned above].
Initially one must use a curved horn of a ram for blowing Shofar. If one does not have such a horn available than the following are the laws of other Kosher horns:
A Kosher horn must contain the following:
- Derive from a Kosher species.
- Not be from a cow or ox.
The ideal Kosher horn is to also contain in addition to the above:
- Curved shape
- Come from a ram
List of Kosher animal horns:
From what age is a ram considered an “Ayal” rather than a sheep?
When a sheep reaches the age of 13 months it is considered an Ayal. If it is below this age then it is still considered a sheep.
Are the horns of female rams [Ewe] initially valid?
Yes. The horns of a female ram are considered valid ram horns.
Is the horn of a mix breed animal Kosher?
If the mix breed comes from both a male and female animal of which their species of Shofar is valid, then it is valid. If however the male or female parent is from a species that their Shofar is invalid, then this Shofar is likewise invalid.
Are the horns of a buffalo valid?
Must one purchase a Shofar that contains a Hashgacha [Rabbinical supervision]?
Yes, as one must verify that the horn comes from a Kosher animal and has fulfilled the above mentioned requirements.
If one only has either a curved non-ram horn or a straight ram horn available which one is better to use to blow Shofar?
Some Poskim rule it is better to use the curved horn. Others rule there is no advantage of one over the other in such a case and one may hence use whichever horn he chooses. Practically it is best to use the curved horn in place of the straight horn of a ram.
 586/1; Michaber 586/1
 Admur ibid; Levush; M”A 586/2; P”M 586 A”A 2; Chayeh Adam 140/2; M”E 586/1; M”B 586/6; Kaf Hachaim 586/10
 Peri Megadim 586 A.A. 2
 The reason: The reason for this is because the horn of a cow and ox is referred to as a “Keren” and not as a “Shofar” as it says in the verse “Bechor Shoro.. Vekarnei Reim Karnav”, and only horns which the Torah considers a Shofar are valid for the blowing. [ibid; M”A 586/2] Vetzaruch Iyun Gadol as the rams horn is also referred to as a Keren [in the Parsha of Akeidas Yitzchak] and nevertheless not only is it valid but it is the best type of Shofar to use.
 586/1; Michaber 586/1
 As the word Shofar comes from the term Shofaros which implies that there are many horns [i.e. Cartilage] within the horn that are able to be peeled off, such as the horns of a ram and goat. [ibid]
 586/3; Rama 586/1
Other Opinions: There are opinions that rule that Bedieved horns of non-Kosher species are valid. [see Peri Megadim 586 A.A. 3]
 The reason: The reason for this is because only Kosher items are allowed to be used to perform Heavenly commands. [Admur ibid; M”A 586/3] This is learned from the law by Tefillin that only Kosher items may be used to make the Tefillin and the entire Torah is connected to Tefillin. [M”A ibid]
 586/2; Michaber 586/1
 The reason: The reason for this is because [the ram was substituted as a sacrifice during Akeidas Yitzchak and thus] we blow using a rams horn to invoke memory of Akeidas Yitzchak. [Admur ibid; M”A 586/1] This implies that we do so to arouse Hashem’s memory of Akeidas Yitzchak and hence bring a merciful judgment. See Gemara R”H 16a “Rebbe Avahu stated: Why do we blow with the horn of a ram? Hashem said “Blow before me the horn of a ram in order so I remember the Akeida of Yitzchak the son of Avraham and consider it as if you also sacrificed yourselves by the Akeida.”
 586/1; Michaber 586/1
 The reason: This is in order to affect the listeners, to subjugate their hearts to G-d through prayer. [Admur ibid; M”A 586/1]
 586/2; As the requirement to use a curved horn is only initially, and Bedieved if one blew using a straight horn he has fulfilled his obligation, and in a case that there are no curved horns available it is defined as Bedieved and one may hence use a straight horn. [ibid]
 Kaf Hachaim 586/2; Mishneh Parah 1/3
 M”B 586/2 in name of Taz; Elya Raba; and Mateh Efraim
 Siddur Yaavetz; Kaf Hachaim 586/15
 Sheilas Yaavetz 1/50; Shaareiy Teshuvah 586/3; Kaf Hachaim 586/11
 The reason: As the Buffalo is considered a species of oxen which is invalid due to being part of the cow species. [ibid]
 Piskeiy Teshuvos 586 footnote 5
 Kaf Hachaim 586/4
Opinion of Admur:
On the one hand Admur 586/2 records the ruling of the Bach that initially one may not use the horns of other animals, and hence it seems a non-ram horn and a straight horn have an equal disadvantage. On the other hand Admur writes that not only are non-ram horns valid Bedieved but even curved horns are valid Bedieved hence implying that curved horns are a greater disadvantage than a ram horn. This is also implied from the fact Admur records that using a ram horn is only a Mitzvah Min Hamuvchar and not an initial requirement from the letter of the law. Vetzaruch Iyun
 Taz 586/1
 As a rams horn is only required for a Mitzvah Min Hamuvchar while a curved horn is initially required from the letter of the law, hence we see that a curved horn is of greater advantage than a rams horn which is straight. [Taz ibid]
 Mamar Mordechai 586/1; Peri Megadim 586 A.A. 1
 As the Michaber lists both the issue of having a ram’s horn and a curved horn in a single sentence with the same level of command. Hence according to the Michaber in Shulchan Aruch [as opposed to the Beis Yosef] there is no advantage of one over the other. This follows the ruling of the Bach that it is only Bedieved allowed to use a non-ram horn and it is not simply a Mitzvah Min Hamuvchar. Hence both a straight horn and non-ram horn are equally initially prohibited and Bedieved permitted, and there is no advantage of one over the other. [Kaf Hachaim ibid]
 M”B 586/5; Kaf Hachaim ibid
The reason: Most Poskim rule a curved horn is required from the letter of the law while a ram horn is merely a custom. [M”B ibid] Alternatively since everyone agrees that there is no problem to use the curved horn, and the Taz holds that one must use the curved horn in such a case one should therefore use the curved horn in order to avoid dispute. [Kaf Hachaim ibid]