Peridynamics (PD) is a generalized continuum theory that is developed to account for long range internal force/moment interactions. PD equations of motion are of the integro‐differential type, and only several closed‐form analytical solutions are available for elementary structures. In this paper, governing equations for stability of Kirchhoff type (shear rigid) plates in the PD framework are derived. For several types of boundary conditions, closed form analytical solutions for the buckling loads are presented. The results are compared with the solutions according to the classical plate theory. A very good agreement between the non‐local and the classical theories is observed for the case of the small horizon sizes which shows the capability of the developed approach.