A procedure is presented for the determination of geometric buckling for regular polygons. A new computation technique, the multiple reciprocity boundary element method (MRBEM), has been applied to solve the one-group neutron diffusion equation. The main difficulty in applying the ordinary boundary element method (BEM) to neutron diffusion problems has been the need to compute a domain integral, resulting from the fission source. The MRBEM has been developed for transforming this type of domain integral into an equivalent boundary integral. The basic idea of the MRBEM is to apply repeatedly the reciprocity theorem (Green’s second formula) using a sequence of higher order fundamental solutions. The MRBEM requires discretization of the boundary only rather than of the domain. This advantage is useful for extensive survey analyses of buckling for complex geometries. The results of survey analyses have indicated that the general form of geometric buckling is = (aN/Rc)2, where Rc represents the radius of the circumscribed circle of the regular polygon under consideration. The geometric constant aN depends on the type of regular polygon and takes the value of π for a square and 2.405 for a circle, an extreme case that has an infinite number of sides. Values of aN for a triangle, pentagon, hexagon, and octagon have been calculated as 4.190, 2.821, 2.675, and 2.547, respectively. Although the discussion is restricted to simple regular polygons, the proposed solution technique based on the MRBEM can easily be applied to many other complex geometries.