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 non-uniformity 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.