Abstract One-way shape memory effect (SME) is not suitable mechanism for application to the repeated actuation of an shape memory alloy (SMA) wire because the host structure does not return to its initial shape after it cools down. In the present study, the two-way SME under residual stress is considered. A structure using the two-way effect returns to its initial shape by increasing or decreasing temperature under an initially given residual stress. A thermo-mechanical constitutive equation of SMA proposed by Lagoudas et al. was employed in the present study. Laminated composite plate and beam are considered as simple morphing structural components. The modeling of plate and beam are based on first-order shear deformable laminated composite plate theory with large deflection and large deformable beam theory respectively. Numerical results of fully coupled SMA–composite structures are presented. The proposed actuation mechanism based on the two-way SMA effect and a simulation algorithm can be used as a powerful morphing mechanism and simulation tool for structures.