Liquid crystal elastomer (LCE) is a special polymer material that combines the properties of rubbers and liquid crystals. It can exhibit soft elasticity with stress plateau and hysteresis due to the mechanical‐director coupling and may be utilized in mechanical energy absorption and dissipation. Herein, some numerical results based on the continuum model of LCE are presented. Using COMSOL, the highly anisotropic loading–unloading behavior of monodomain LCE samples is studied in some detail. When the loading axis is close to the initial LC alignment, the mechanical behavior of the LCE is similar to regular rubber, hyperelastic with weak rate dependences. However, if the loading axis is far from the initial LC alignment, stripe domains appear with apparent stress plateau and a large loading–unloading hysteresis. Consequently, rather big residual strains and stresses can be observed after unloading. Such samples have much stronger rate dependence, much higher efficiency of energy absorptions, and much bigger mechanical energy damping capacity. Thus, it is important to program the initial LC alignment according to the external loading directions to maximize the mechanical energy absorption and dissipation of LCEs.