A theory is presented for the wrinkling of honeycomb sandwich beams, which satisfies the governing elasticity equations for the orthotropic core and laminated faces. A single eighth order ordinary differential equation is obtained which is solved by assuming a simple sine function for the displacement of the buckled face. Minimum critical loads are found numerically, and results are given for typical beams which show the dependence on face plate thickness and core thickness. A comparison is made with other approximate solutions.