A viscous-inviscid interaction scheme is presented for computing steady, two-dimensional, incompressible, laminar and turbulent flows over a rearward-facing step. The scheme utilizes the boundary-layer equations for the region of viscous flow and the Laplace equation for streamfunction in the region of inviscid flow. The boundary-layer continuity and momentum equations are solved inversely in a coupled manner using an improved finite-difference calculation procedure. For the inverse solution procedure, the displacement thickness, rather than the edge velocity, is specified as a boundary condition. The streamwise convective term is altered in regions of reversed flow to permit marching the solution in the streamwise direction. The inviscid flow is computed by solving numerically the Laplace equation for streamfunction using an ADI finite-difference procedure. The viscous and inviscid solutions are matched iteratively. The present viscous-inviscid interaction scheme appears to be the first interaction procedure to employ a finite-difference formulation for the reversed flow region in a rearward-facing step flow. The calculation scheme is evaluated for one fully laminar and three turbulent rearward-facing step flows. A part of the study is devoted to the development of a simple algebraic length scale turbulence model for flows behind a rearward-facing step. A turbulence model which utilizes a solution to a transport equation for turbulence kinetic energy is also evaluated. The predictions are compared with experimental data and other available predicted results. Agreement is generally favorable but the need for more research on the accurate prediction of turbulence phenomena in the separated and redeveloping flow regions downstream of the step is evident;Consideration is also given to the applicability of the boundary-layer equations to two-dimensional channel expansion flows with developed inlet velocity profiles. In such flows, no inviscid flow region can be identified so that the viscous-inviscid interaction procedure is not applicable. In the present study, predictions of laminar flows of this type using the inverse boundary-layer numerical method are shown to be in good agreement with existing Navier-Stokes solutions and experimental measurements;In addition, simple separation bubble flows occurring on smooth surfaces (without step) are also predicted using the boundary-layer equations with and without viscous-inviscid interaction. These predictions are compared with experimental measurements and other numerical predictions.