The local buckling of stiffened panels is one of possible failure modes and concerned by engineers in the preliminary design of lightweight structures. In practice, a simplified model, i.e., a rectangular plate with elastically restrained along its unloaded edges, is established and the Ritz method is usually employed for solutions. To use the Ritz method, however, the loaded edges of the plate are usually assumed to be simply supported. An empirical correction factor has to be used to account for clamped loaded edges. Here, a simple and efficient method, called the quadrature element method (QEM), is presented for obtaining accurate buckling behavior of rectangular plates with any combinations of boundary conditions, including the elastically restrained conditions. Different from the conventional high order finite element method(FEM), non-uniformly distributed nodes are used, and thus the method can achieve an exponential rate of convergence. Formulations are worked out in detail. A computer program is developed. Improvement of solution accuracy can be easily achieved by changing the number of element nodes in the computer program. Several numerical examples are given. Results are compared with either existing solutions or finite element data for verifications. It is shown that high solution accuracy is achieved. In addition, the proposed method and developed computer program can allow quick analysis of local buckling of stiffened panels and thus is suitable for optimization routines in the preliminary design stage.