This paper investigates the compaction of pharmaceutical powders using different shapes of punches. We introduce a model of mechanical behaviour Drucker-Prager Cap (DPC), using the approach of compressible continuous media. The model parameters that are depending on the material density, were identified from experimental data and a calibration process was applied on Microcrystalline Cellulose (MCC) powder. In addition, the mathematical formulation of the boundary problem of compaction in rigid tools brings back to an optimization problem with constraint, which is solved by finite element method. The Drucker-Prager Cap model, which is implemented in Abaqus/Standard software, was employed using a user subroutine, USDFLD. Three kinds of typical pharmaceutical tablets are considered: flat-face tablet and concave face tablet with two different depths. Results of simulations of die compaction cycle as compression, decompression and ejection, reproduce the powder compaction process for the studied shaped punches. The effects of the punch's shape on the compaction process were observed on the distribution and the maximum of stress and density in the compact. Examination of the density gradient according to the shape, suggests a capping tendency, which increases with the punch depth. This study illustrates the potentiality of the FEM method, which could be used as an efficient tool to predict the density and the stress distributions into shaped compacts and to provide a diagnostic of the capping problems. (C) 2013 Elsevier B.V. All rights reserved.