The flow and shape evolution during the compression of a finite amount of a Bingham plastic is investigated by means of numerical simulations. The problem relates to the popular compression test used for the theological characterization of non-Newtonian fluids. The flow is modelled in Lagrangian coordinates using the Papanastasiou regularization for the Bingham plastic and a mixed-Galerkin finite element method. Simulations have been performed for compression under both constant load and constant velocity. Results for various Reynolds and Bingham numbers are presented and discussed. (c) 2007 Elsevier B.V. All rights reserved.