A method is described for solving an inverse design problem to find the unassembled, stress-free component shapes of a structure thatis integrally actuated with shape memory alloy (SMA) actuators. Morphing and multifunctional structures are of interest in the aerospace industry becasue of the potential for improving structural and aerodynamic performance across multiple operating conditions. The focus of this work is on structures that are morphed with SMA flexural actuators. For the case where the geometry is known for unassembled components, assembly can be simulated to find the assembled shapes of the morphing structure. In the usual design case, however, only the desired shapes as assembled are known in multiple actuation states, and the corresponding unassembled shapes must be determined by an iterative solution process. An iterative finite element analysis approach to this problem is reported here. First an initial guess for the unassembled shapes is made and assembly is simulated with the finite element method. The resulting shapes are found for both SMA phases and compared with the desired shapes. A gradient-based optimization method is employed to update the initial geometry and iteration continues until the desired shapes are achieved. A simplified method of modeling the SMA material behavior is used for computational efficiently. It is found that this approach provides a practical way to solve the inverse design problem for structures that are integrally actuated with SMA material.