Buckling of stiffened plates with arbitrary stiffener orientations and with constant or stepwise constant plate thickness are studied. The stiffeners are sniped at their ends and they are not subjected to an external loading. The main objective of the present paper is to present and validate an approximate, semi-analytical computational model for such plates subjected to in-plane loading. The deflections are represented by trigonometric functions, defined over the entire plate. The method allows for a very efficient analysis of the structural response and the subsequent design of such plates. Estimation of the buckling strength is made, using the von Mises' yield criterion for the membrane stress as the strength criterion. The formulations derived are implemented in a Fortran computer code, and numerical results are obtained for a variety of plate and stiffener geometries. The model may handle complex plate geometries, by using inclined stiffeners to enclose irregular plate shapes. Relatively high numerical accuracy is achieved with low computational efforts. The results are, in most cases, found to be conservative compared to finite element analysis results. The model does not account for the reserve strength beyond the elastic buckling load.