The Ruling Of Praying With Bare Shoulders
Covering the `awrah is one of the validity conditions of prayer. Covering the `awrah while praying for both men and women is obligatory due to unanimous agreement of the jurists . Therefore, prayer without covering the `awrah is invalid. Almighty Allah says:
O children of Adam, take your adornment at every masjid… (Al-`Araf 7:31)
“Covering the `awrah from view with something that does not show the skin is obligatory and is a condition of prayer being valid.” This is the view of Ash-Shafa`i.
Ibn Hajar said: “The majority are of the view that covering the `awrah is one of the conditions of prayer.” (Fath Al-Bari)
Regarding covering the shoulders, It is not obligatory for a man to cover his shoulders or shoulder while praying, but it is mustahab to do so as an adornment and out of respect for the prayer and the fact that he is standing before his Lord, may He be glorified and exalted; but if he prays with his shoulders or shoulder blade bare, his prayer is valid.
To know more about such rule, watch this short talk with Dr. Muhammad Salah.
Source: Huda Youtube Channel.