The results of an analytical study of the nonlinear response of flat and curved panels subjected to pre-existing, nondestabilizing lateral pressure and thermal loads and to mechanical edge loads are presented. The mechanical loads include uniaxial compression loads and combinations of uniaxial compression and transverse tension or compression loads that are increased monotonically into the postbuckling response range of the panels. The structural model used to analyze the panels is based on a higher order shell theory that includes transverse-shear flexibility, initial geometric imperfections, and von Karman_type geometric nonlinearities. The edges of a panel are modeled as simply supported edges with the displacement normal to the edge face either unrestrained or fully restrained. Results are presented for transversely isotropic single-layer panels and three-layer sandwich panels that illustrate how the temperature field, initial imperfections, lateral pressure loads, and mechanical edge loads interact to change the character of the nonlinear panel response. Some response curves are presented that have classic unstable, asymmetric bifurcation behavior and intense snap-through instabilities. Other results show that, for some cases, these interactions can reduce the intensity of snap-through instabilities and even eliminate this form of instability altogether for certain ranges of loading and structural parameters. In addition, results are presented that show how transverse-shear flexibility affects the interactions of the temperature field, the initial imperfections, the lateral pressure loads, and, thus, the character of the nonlinear panel response. One important finding of the present study is that linear bifurcation buckling analyses may not indicate adequately the onset of significant nonlinear deformations of a geometrically perfect, shallow curved panel for certain combined mechanical loading conditions. This finding may affect current preliminary design practice.