A numerical study is conducted on the pressure-driven laminar flow of an incompressible viscous fluid through a rectangular channel subjected to a spanwise rotation. The full nonlinear time-dependent Navier–Stokes equations are solved by a finite-difference technique for various rotation rates and Reynolds numbers in the laminar regime. At weak rotation rates, a double-vortex secondary flow appears in the transverse planes of the channel. For more rapid rotation rates, an instability occurs in the form of longitudinal roll cells in the interior of the channel. Further increases in the rotation rate leads to a restabilization of the flow to a Taylor–Proudman regime. It is found that the roll-cell and Taylor–Proudman regimes lead to a substantial distortion of the axial-velocity profiles. The specific numerical results obtained are shown to be in excellent agreement with previously obtained experimental measurements and theoretical predictions.