AbstractFinite‐difference and finite‐element techniques have been used to calculate the steady laminar flow over a flat plate normal to an air stream, up to a Reynolds number, Re, based on the plate half‐width, of 100. The boundary conditions simulate a central splitter plate downstream of the body, to prevent vortex shedding, so the flow is characterized by a closed recirculation region which grows with increasing Re but at Re =O(100) is very similar in size to the turbulent recirculating region that occurs in the corresponding high Reynolds‐number flow. Motivation came, in part, from the increasing efforts of turbulence modellers to calculate complex turbulent flows (containing elliptic regions) and our belief that the numerical methods commonly employed for such work can be inaccurate. The predictions are compared with each other and with some expectations based on classic solutions of the Navier‐Stokes equations, and the nature of the numerical errors is demonstrated. It is concluded that effort comparable with that expended in developing turbulence models should be directed to developing higher‐order numerical methods, before the numerical accuracy of predictions of, for example, bluff‐body flows can be made sufficiently high to sustain detailed discussion of the adequacy of turbulence models in su