Loosely bound membranes exhibit an unusual elastic response when pinch
ed together by optical tweezers, locally unbinding to a large intermem
brane distance. Tweezing a stack of many bound membranes produces extr
eme local swelling in the vicinity of the tweezing point. We introduce
a model that incorporates bending elasticity, fluctuations, and inter
membrane interactions to calculate the membrane profiles subject to a
local pinch. Theoretically, we find strongly overshooting profiles in
agreement with experiment. We predict scaling behavior of the overshoo
t with the pinch strength and size.