Abstract: The face sheets of sandwich beams tend to wrinkle under in-plane compressive stress. Fine meshes and significant computational costs are required when wrinkling stresses are computed using the traditional finite element method. Additionally, the frequently used simple formulas cannot provide accurate results. Hence, an accurate and efficient method for computing the wrinkling stress of sandwich beams is required. In this study, a new method for computing the wrinkling stress by solving a tridiagonal system of equations was proposed. Based on the feature that the wrinkling displacements decay from the face sheets towards the core, the decaying curves were discretized through piecewise linear interpolations. The unknowns of the equations were the discretized decaying curves. Moreover, a simultaneous diagonally-dominant tridiagonal system of equations was constructed to compute wrinkling stress, based on the relationship between the work and strain energy during the wrinkling. The wrinkling stresses of typical sandwich beams were computed and compared with those using the finite element method and the analytical method. The comparison shows that the present method agrees well with the two methods. Moreover, the present method is significantly more efficient than the finite element method. The number of unknowns in this method is only a few hundredths of that in the finite element method. In addition, the proposed method solely involves solving linear equations, eliminating the need for eigenvalue computations or iterative processes. There is no additional workload involved in solving the wrinkling stress of sandwich structures with layered material cores using this method.