The Beatles - A Day in The Life: July 14, 1965 (Wednesday)
The term "plastic soul" can be heard by Paul using the phrase on the compuliation album The Beatles Anthology 2, after the the first take of "I'm Down" which they recorded on July 14, 1965, and was probably inspired by Little Richards. "Plastic soul, man, plastic soul," he says. The Beatles had been kicking around different ideas for the title, and then settles on it after their photographer, Robert Freeman, inadvertently created an elastic effect on one of their photos he projected it onto a 12' x 12' peice of cardboard.
Source: Beatles Vs. Stones by John McMillian