Secondary flow in cone‐and‐plate viscometers is studied by numerical integration of the equations of motion for steady incompressible flow of Newtonian fluids. Solutions over wide ranges of the two principal parameters, Reynolds number and gap angle, yield detailed information on the flow fields and elements of the rate of deformation tensor. Secondary flows are shown to cause large deviations in certain elements of the rate of deformation at Reynolds numbers more than an order of magnitude lower than those at which the torque is appreciably changed. Comparisons are given with prior analytical and experimental work.