Yawning and burping during Davening:
One may not burp or yawn during Shemoneh Esrei. If one willingly burps or yawns during Shemoneh Esrei he is from amongst the haughty individuals. If one gets the urge to yawn [and is unable to control it], then he is to place his hand over his mouth, in order so his open mouth not be apparent to others. [According to some Poskim, the same applies if one has the urge to burp and is unable to control it, that he is to place his hand over his mouth. Other Poskim however rule that by a burp, one is not required to cover his mouth. Practically, one is to be stringent.]
Sneezing during Davening:
One is not to yawn or burp during Davening, and if he feels an urge to do so, he is to cover his mouth.
May one burp or yawn in the parts of Davening that precede Shemoneh Esrei?
The above prohibition against burping or yawning is in reference to Shemoneh Esrei. There is no recorded prohibition do so during other parts of Davening, even though it may not be appropriate.
Does one need to cover his mouth during a yawn or burp if he is Davening in private?
May one continue saying the words in middle of yawning?
Which hand is one to use to cover his mouth?
Some say he is to use his right hand.
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 Admur 97:1; Michaber 97:1; Braisa Brachos 24b; Kitzur SHU”A 18:9; Ketzos Hashulchan 20:9
 Literally “Yigaheik, which refers to air that is expelled from one’s body into one’s mouth as a result of satiation.” [Admur ibid; Taz 97:1; Elya Raba 97:1; Rashi Brachos ibid; See Kaf Hachaim 97:1]
 Literally “Yipaheik, which refers to opening the mouth like a person who desires to sleep, or has awaken from sleep.” [Admur ibid; Taz 97:1; Rashi Brachos ibid; See Kaf Hachaim 97:1]
 Admur ibid; Tur ibid; Brachos ibid
 Aruch Hashulchan 97:1-2, otherwise it is not considered an Oness, and he must control it. Vetzaruch Iyun from Brachos ibid.
 Admur ibid; Michaber ibid; Brachos ibid; Rashi Brachos ibid; Rosh Brachos 3:39; Yerushalmi Brachos 3:5
 Tur 96 “If one needs to do them”; Maharsha Brachos ibid; Levush 97; Soles Belula 1; Implication of Chida in Kesher Gudal 12:27; Beis Oved 43; Kitzur SHU”A 18:9; Aruch Hashulchan 97:1; Kaf Hachaim 96:2
 Implication of Admur ibid, Michaber ibid, and Brachos ibid, who write only the case of “Yawn”; Elya Raba 97:1; Mamar Mordechai 97:1; Nehar Shalom 97:1; P”M 97 M”Z 1; M”B 97:1
 The reason: Some Poskim rule one is not required to cover his mouth in middle of Shemoneh Esrei, if he has a desire to burp, and only by a yawn, in which one stretches his mouth open very much, is covering the mouth required.
 Kaf Hachaim ibid
 Admur 103:3; Michaber 103:3; Brachos 24b
 The reason: As sneezing is pleasant for a person, and just as G-d is giving him a pleasant pleasure down here, so too He is giving him blessing above, to fulfill his will and requests. [Admur ibid; Rav Zeira Brachos ibid and Rashi ibid]
 See Yerushalmiu Brachos 3:5 “I saw that when Rebbe yawned and sneezed, he covered his mouth”
 Tiferes Shmuel on Rosh ibid; Kaf Hachaim 97:3
 Makor Chaim 97
 Orach Neman 97:1; Piskeiy Teshuvos 97:1