This paper presents solutions to the inelastic buckling problem of a thin flat rectangular isotropic panel under uniform uniaxial in-plane compression. The case of boundary conditions studied is a panel clamped along three edges with one simply supported longitudinal edge (CCCS). Stowell’s and Bleich’s plasticity approaches are used in deriving the governing equations. A theoretical formulation based on Taylor’s series is used in estimating the shape function which satisfied the boundary conditions and resulted to a peculiar shape function for the CCCS panel. Values of the panel buckling coefficient are calculated for aspect ratios from 0.1 to 2.0 at intervals of 0.1. The results are compared with the solutions from previous studies and the percentage differences are found to be consistent. Therefore, the proposed method can be used for the inelastic buckling analysis of thin flat rectangular isotropic panels with mixed boundary conditions subjected to uniform uniaxial in-plane loads.