Nonlinear behavior of sandwich panels with a transversely flexible core is presented. The panel construction is general and consists of two face sheets metallic or composite laminated symmetric, and a “soft” core made of foam or a low strength honeycomb. The study is based on a high-order nonlinear formulation that includes the influence of the transverse flexibility and shear resistance of the core on the panel behavior, so allowing for interaction between the faces through the core thickness. The solutions obtained are general and are not based on separation of the nonlinear response on the local and global modes as commonly used in the literature on sandwich structures. The governing equations along with the appropriate boundary and continuity conditions are presented and the solution approach is outlined. The formulation is of a mixed form causing the classical solution methods used in the nonlinear structural analysis to be abandoned in favor of the more general techniques. The path-following algorithm devised is based on the natural parameter as well as the arclength continuation techniques. The quasi-Newton framework with line searches is used to solve both the nonlinear equilibrium equations and the bordered equations arising in the case of applying the arclength method. The capabilities of the formulation are demonstrated for various cases including action of a concentrated load at the mid span of the panel, loading of the panel by end couples, and compression of an unsymmetric sandwich panel by longitudinal forces. It is shown that the transverse flexibility of the core is responsible for the interaction between global and local deformation modes. Comparison with linearized buckling results is presented and conclusions are drawn.