Vesicles composed of diblock copolymers, or polymersomes, have proven to possess numerous applications ranging from drug delivery to catalytically driven nano-motors. The shape of a polymersome can be responsive to external stimuli, such as light or solvent. Molecular dynamics simulations reveal that the shape change upon the contraction of the inner volume of a polymersome vesicle occurs in two separate regimes-a stretching regime and a bending regime. The barrier is shown to be dependent on the solvent environment. These results suggest that tailoring the bending modulus of polymer membranes can be used as a design methodology to engineer new stimuli-responsive vesicles.