In this research, the thermomechanical responses of shape memory alloy (SMA) actuators and their applications in the shape adaptive structures combining strip SMA actuators are investigated. The numerical algorithm of the three-dimensional (3-D) SMA thermomechanical constitutive equations based on Lagoudas model is developed to analyze the unique characteristics of a SMA strip. The Green-Lagrange strain-displacement relationships are adopted to consider the large displacements, large strains, and material nonlinearity. For the numerical results presented in this article, the ABAQUS finite element program has been utilized with an appropriate user supplied subroutine (UMAT) written by FORTRAN for modeling a SMA strip and host elastic structure elements. In this model of a SMA strip, the shape memory effect is restricted to one-way applications. Numerical results show that an SMA strip actuator can generate enough recovery force to deform the host structure and sustain the deformed shape subjected to large external load, simultaneously. But, there are some difficulties found in designing reversible shape adaptive structures with this actuator, even if the SMA strip is coupled to an elastic structure which compels the SMA to recover the initial condition.