If you ate while walking, you may say Birkat Hamazon while walking.
If you sat while eating you have to sit while saying Birkat Hamazon
If one didn't eat in a house - or one ate in the house of a non-Jew, one replaces the 6th הָרַחֲמָן with:
Source: Kitzur Shulchan Aruch 68:9, 10
Tuesday, 26 Tevet 5770
Please daven for a complete recovery of 3 year old Chaim Ovadya ben Sara