Humans and animals utilize stiffness-altering faculties and elastic structures embedded within their musculoskeletal systems which allow them to manipulate and locomote within natural, dynamic environments. Hence, arming soft robots with mechanisms that accord them stiffness and elasticity is a pivotal step towards realizing machines closer to biological structures. While there is research in the domain of variable stiffness in soft robotics, variable elasticity is an area that is yet to be thoroughly investigated. This article presents the design, manufacturing, and performance demonstration of a novel device for addressing this key challenge: enabling a mechanism to reversibly modify its elasticity along a specific direction of motion. The device which we call the variable elasticity soft module (VESMo) is based on low-cost commercially available polymers and operates via pneumatic actuation. A significant application of our device is its capability of storing and returning energy of adjustable levels of intensity, like the role of biological springs in animals. Our experiments verify that the spring constant of the VESMo can be increased by more than 194% depending on the properties of the constitutive polymers and thepressure effected by the vacuum regulator. Finally, the performance of the device in two demonstrative mechanisms is presented.