A new method of analysis based on the consideration of equilibrium and a physically acceptable dis­placement field is proposed in this paper to investigate the fully plastic behaviour of a clamped circular plate which is loaded axisymmetrically by a rigid hemispherical-headed punch. The attention is confined to the range of loads for which the central deflection of the plate exceeds the plate thickness, and the effect of the induced membrane forces is duly allowed for in the theoretical framework to obtain a realistic ex­pression for the load-deflection relation in the plastic range. When the central deflection becomes suf­ficiently large, the deformation of the plate occurs essentially under membrane stresses alone, and the analysis then becomes similar to the one presented earlier by the author for a material that work-hardens iso­tropically according to the Ludwik power law. Since the considered range of deflections is sufficiently large, the material is assumed to be rigid/plastic, and the work-hardening of the material is disregarded as a neces­sary first step towards a more general solution. The complete load-deflection relation is presented in a graph­ical form for the situation where the punch radius is equal to the radius of the plate.