Is it permissible to walk across in front of someone who is praying Salaat?
Praise be to Allah.
It is not permissible to walk across in front of someone who is praying, and it is a great sin, as the Prophet (peace be upon him) said (approximate translation of meaning is):
"If the one crossing in front of a praying person knew what sin is upon him, it would be better for him to wait forty than walk across." Abu Al-Nadhr (one of the narrators of the hadith) said: I don't know whether he said forth days, months, or years. (Bukhari)
Imam Al-Bukhari (R) has named the chapter in which he brings the hadith as follows: Chapter on the sin of walking across in front of a praying person.
When the praying person is the leader in the prayer or praying alone, and he has a sutrah( some object like a peice of wood) in front of him, then walking across in between him and his sutrah is not permitted. However, if he is praying without a sutrah, it is not permissible to walk across in between him and his place of prostration. For the followers (in a jamaa'ah prayer), the leader's sutrah is enough for them. Based on this, it is permissible to walk through in front of a row if need be.
And Allah knows best.