Composite laminates with optimized curvilinear fibre paths, which are manufactured by the Variable Angle Tow (VAT) placement technique, have previously been shown to outperform straight fibre laminates for some load cases subject to certain buckling criteria. Strength analysis and optimum design of VAT laminates in previous research have mainly relied on finite element modelling (FEM). In this study, we present analytical models for the prebuckling and buckling analysis of VAT plates, which is applicable to general loading cases with mixed boundary conditions. The models are derived from the principle of minimum complementary energy, considering both prescribed force and displacement boundary conditions. The innovation of this work is in the implementation of the Rayleigh- Ritz solution to the plane elasticity problem of variable-stiffness plates under uniform end shortenings, in which case the unknown boundary stresses are difficult to determine and the in-plane stress/displacement fields are non-uniform. Numerical results for both balanced and unbalanced VAT plates are demonstrated and validated by FEM (ABAQUS). The effects of extension-shear coupling (A16;A26) and bending-twisting coupling (D16;D26) on the prebuckling and buckling analysis of VAT plates are investigated. The study of VAT plates under shear loading and combined loadings are shown to highlight the methods. The proposed models in this article are of particular interest in the design of VAT plates. This study also underpins future development of the Rayleigh-Ritz method for postbuckling analysis of VAT plates. © 2012 AIAA.