An adaptive multiresolution scheme is proposed for the numerical ă solution of a spatially two-dimensional model of sedimentation of ă suspensions of small solid particles dispersed in a viscous fluid. This ă model consists in a version of the Stokes equations for incompressible ă fluid flow coupled with a hyperbolic conservation law for the local ă solids concentration. We study the process in an inclined, rectangular ă closed vessel, a configuration that gives rise a well-known increase of ă settling rates (compared with a vertical vessel) known as the ``Boycott ă effect''. Sharp fronts and discontinuities in the concentration field ă are typical features of sedimentation phenomena. This solution behavior ă calls for locally refined meshes to concentrate computational effort on ă zones of strong variation. The spatial discretization presented herein ă is naturally based on a finite volume (FV) formulation for the Stokes ă problem including a pressure stabilization technique, while a ă Godunov-type scheme endowed with a fully adaptive multiresolution (MR) ă technique is applied to capture the evolution of the concentration ă field, which in addition induces an important speed-up of CPU time and ă savings in memory requirements. Numerical simulations illustrate that ă the proposed scheme is robust and allows for substantial reductions in ă computational effort while the computations remain accurate and stable.