Shape-memory alloys can sustain relatively large strains and fully recover without noticeable residual strains. This is referred to as superelasticity. We have been studying quasi-static and dynamic buckling of relatively thin circular cylindrical shells consisting of shape-memory alloys in order to understand the response when used as the core of the sandwich structures. The work consists of experimental characterization of the buckling process, as well as numerical simulation. For comparison, we have also studied both dynamic and quasi-static buckling of aluminum tubes of similar dimensions. This presentation will focus on numerical simulation of dynamic buckling of these tubes and correlation with experimental observations.