Structures made of variable stiffness (VS) composites possess a rich design space for bistable configurations that demonstrate different values of curvatures and out-of-plane displacements. In this study, several VS composites are investigated which can yield cylindrical bistable shapes similar to those generated from unsymmetrical cross-plies. Such configurations have been found favorable as a component for certain morphing applications. A semi-analytical model based on the Rayleigh-Ritz approach is presented to calculate the thermally induced multistable shapes as well as the snap-through forces particularly taking into account the curvilinear paths of VS composites. A nonlinear finite element analysis is performed to check the accuracy of the semi-analytical method. Cylindrical shapes generated from VS laminates and the corresponding straight fiber cross-ply laminates are analyzed and compared. The snap-through forces are subsequently calculated and compared for different VS laminates and the straight fiber cross-ply. It is observed that certain VS composites have a significant reduction of snap-through forces but with a marginal difference in out-of-plane displacement as compared to the corresponding straight fiber cross-ply laminate.