Cold and hot isostatic compaction of monosized metal powders is analysed within the framework of viscoplastic theory for particles packed both in a regular and a random manner. The problem of local contact between spherical particles is analysed first by drawing upon recent detailed numerical studies of spherical indentation of power law plastic and creeping solids. The compaction process is then modelled as a self-similar contraction of unit (average) cells, in contrast to commonly used phenomenological assumptions, yielding a simple but rigorous relation between the densification density and centre-to-centre approach of adjacent powder particles. The resulting densification formulae are easy to apply and the influence of hardening and creep parameters appears in concise form. Predictions are compared with discriminating experimental data for a variety of different powder materials, both in the cold and a hot state, and the agreement is good for a relative density increase of up to 30%. Copyright (C) 1996 Acta Metallurgica Inc.