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A new yield criterion for metal powder compaction based on continuum mechanics has been proposed. It includes three parameters to characterize the geometric hardening of powder compact and strain hardening of incompressible metal matrix. The elasto-plastic finite element method to describe compaction of metal powders has been formulated using the new yield criterion. The values of parameters in the yield criterion could be determined through cold isostatic pressing (CIP). The finite-element method was used to simulate compaction behaviour of copper powders of different shape and mean particle size.