An inflatable penile prosthesis of the present invention includes a cylinder that has an external wall that defines a pressure chamber. That external wall preferably incorporates a number of corrugations that extend in a longitudinal direction of the cylinder. In a preferred embodiment, the external wall of the cylinder is formed of a polyurethane or of a material having a modulus of elasticity greater than that of silicone. The corrugations enable the cylinder to move from a small, deflated diameter to a much greater diameter in the inflated state.