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Abstract Locomotion is a critically important topic for soft actuators and robotics, however, the locomotion applications based on two-way shape memory polymers (SMPs) have not been well explored so far. In this work, a crosslinked poly(ethylene-co-vinyl acetate) (cPEVA)-based two-way SMP is synthesized using dicumyl peroxide (DCP) as the crosslinker. The influence of the DCP concentration on the mechanical properties and the two-way shape memory properties is systematically studied. A Venus flytrap-inspired soft actuator is made by cPEVA, and it is shown that the actuator can efficiently perform gripping movements, indicating that the resultant cPEVA SMP is capable of producing large output force and recovering from large deformations. This polymer is also utilized to make a self-rolling pentagon-shaped device. It is shown that the structure will efficiently roll on a hot surface, proving the applicability of the material in making sophisticated actuators. With introducing an energy barrier, jumping can be accomplished when the stored energy is fast released. Finite element simulations are also conducted to further understand the underlying mechanisms in the complex behavior of actuators based on cPEVA SMP. This work provides critical insights in designing smart materials with external stimulus responsive programmable function for soft actuator applications.