Relatively rigid plates making up the outer 50 to 100 km of the Earth are steadily separating from one another along narrow globe-circling zones of submarine volcanism, the oceanic spreading centers. Continuity requires that the viscous underlying material rise beneath spreading centers and accrete onto the steadily diverging plates. It is likely that during the rise the viscosity changes systematically and that the viscous tractions exerted on the plates contribute to the unique pattern of submarine mountains and earthquake faults observed at spreading centers. The process is modeled by viscous creep in a wedge-shaped conduit (with apex at the sea floor) in which the viscosity varies as rm where r is distance from the apex and m is a parameter. For these conditions, the governing differential equations take a simple form. The solution for the velocity is independent of r and of the sign of m. As viscous stresses vary as rm-1, the pattern of stress on the conduit wall is sensitive to viscosity variation. For negative m, the viscous pressure along the base of the conduit is quite uniform; for positive m, it falls toward zero in the axial region as the conduit base widens. For small opening angles, viscous forces push the plates apart, and for large ones, they oppose plate separation. Though highly idealized, the solution provides a tool for investigating tectonic processes at spreading centers.