Ryan gives the POWs the order to strip off their months-old clothes and burn them, in order to force the corrupt camp commandant to issue the fresh clothes he's hoarding for the Italian Black Market. Aside from the overall humor of naked guys, the way both Major Fincham and Captain Oriani respond to the situation adds to the humor.
Fincham: Parade! ... (voice goes up an octave) Strip!
And the camp's priest Costanzo refuses to take off his priestly collar and underrobe, claiming "As a man of the cloth, I take my vow seriously!"