For highly concentrated suspensions which show a compressive yield value, a mathematical model to simulate batch testing in the compression range, is shown in this paper, analyzing the problem of the compression zone and the plug zone and the computer modeling with the simulation language Matlab. The equation of the mathematical model in the compression zone is a partial differential equation of the parabolic type and was originally proposed in the field of soil mechanics. The paper shows that an analytical solution is not possible. In order to simulate the proposed model, the boundary and the initial conditions, and the constitutive relations must be known. These are deduced from the Michaels and Bolger model. A finite difference method is applied to obtain the solids pressure, sedimentation velocity and solids concentration at different distances and times. The simulation program was determined to test if the values obtained in the computation process are similar to the experimental ones. (C) 1998 Elsevier Science Ltd. All rights reserved.