The initial buckling load of flat trapezoidal plates of special orthotropy when loaded in axial compression is determined. Two types of boundary condition are considered: (a) the plate is clamped at one end and free on the other sides; (b) the plate is clamped along opposite ends and free along the sloping sides. The problem is twofold; determining the buckling load and providing a comprehensive parametric understanding of the buckling behaviour. An affine transformation scheme is infused into the solution process such that a minimum number of parameters remain. Using the potential energy functional, the problem of finding the buckling load is then solved by the finite element method. The results are presented for various rigidity ratios of the composite plates. It is observed that increasing the generalized rigidity ratio caused an increase in the stability of the plate.