The response of a spatially non-uniform suspension of spheres to several forcing agents - forces and torques applied to the spheres, and an imposed simple shear - is studied numerically for Stokes flow conditions. While the standard results are recovered in the uniform case, it is found that the nonuniformity of the particle probability distribution gives rise to qualitatively new features. For example, the rheological behavior of the system cannot be described solely in terms of an effective viscosity; a relative velocity between particles and fluid can arise; the particles can either lead or lag the local angular velocity of the fluid elements. It is shown that a mixture effective viscosity can be calculated for all three cases with mutually consistent results. In a subsequent paper the present results will be used to derive in a systematic way closure relations for an averaged-equations description of the suspension. (C) 2000 Elsevier Science Ltd. All rights reserved.