A general computational approach is presented for numerical modeling of viscous flow in baffled, impeller-stirred-tank reactors. A multiblock, body-fitted grid structure facilitates modeling of various impeller and baffle designs, and a new procedure offers averaged velocity data from a complex 3-D CFD dataset. Impellers are modeled precisely, eliminating the need for inputting experimental velocity data for boundary conditions. The method can be used quickly to obtain extremely detailed flow computations at a fraction of the cost of computing unsteady moving grid solutions. A steady-state computational approach that neglects the relative motion between impeller and baffles yields numerical results comparably accurate to full unsteady computations for laminar flow at a fraction of the time and expense. The approximate steady-state method is used to predict power requirements of a Rushton turbine in laminar flow. An unsteady, moving grid technique provides time-accurate solutions for the pow inside an impeller-stirred reactor with side-wall baffles. These computed results are compared with those using the approximate steady-state method and with experimental measurements. The unsteady, moving gild method uses two different initial conditions : one starting from rest and the other starting from an approximate steady-state solution obtained at the starting position of the impeller relative to rite baffles. For unsteady simulations of laminar flow in stirred vessels, the final operating condition call be achieved much more efficiently if the solution obtained from the steady-state procedure is used as an approximate initial condition.