A computationally efficient method for elastic buckling and buckling strength analysis of biaxially loaded, stiffened plates with varying, stepwise constant thickness, are presented. The stiffeners may be sniped or end-loaded (continuous), and their orientations may be arbitrary. Both global and local plate buckling modes are captured. The method is semi-analytical and makes use of simplified displacement computations that involve the elastic buckling load (eigenvalue), determined using a Rayleigh-Ritz approach, and finally stress computations using large deflection theory in combination with strength assessment using von Mises' yield criterion applied to membrane stresses. The displacements are represented by trigonometric functions, defined over the entire plate. The method is implemented into a Fortran computer code, and numerical results, obtained for a variety of plate and stiffener geometries, are compared to fully nonlinear finite element analysis results.