The concept of an equivalent solid material is used to obtain elastic-plastic solutions for circular plates under uniform pressure. Plates with elastically constrained outer edges are considered for the entire range of constraint stiffnesses.Results are obtained for plates perforated in a regular triangular pattern over the entire range of ligament efficiencies used in design.Since such plates may be supported by shells having limited yield moments, solutions are also given for an arbitrary edge moment support.In addition to the limit load results, solutions are given for the pressure at initial edge yielding and initial central yielding, for the elastic-plastic moment distributions, and for the plate deflections.