Numerical computations of the steady, two-dimensional, incompressible, uniform velocity but stably stratified flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the stratification is weak enough to avoid occurrence of the gravity wave motions familiar in more strongly stratified flows over obstacles. The nature of the flow is explored for channel half-widths, H, in the range 5 [les ] H [les ] 100, for Reynolds numbers, Re, (based on body half-width and the upstream velocity, U) up to 600 and for stratification levels between zero (i.e. neutral flow) and the limit set by the first appearance of waves. The fourth parameter governing the flow is the Schmidt number, Sc, the ratio of the molecular diffusion of the agent providing the stratification to the molecular viscosity. For cases of very large (in the limit, infinite) Sc a novel technique is used, which avoids solving the density equation explicitly. Results are compared with the implications of the asymptotic theory of Chernyshenko & Castro (1996) and with earlier computations of neutral flows over both flat plates and circular cylinders. The qualitative behaviour in the various flow regimes identified by the theory is demonstrated, but it is also shown that in some cases a flow zone additional to those identified by the theory appears and that, in any case, precise agreement would, for most regimes, require very much higher Re and/or H. Some examples of multiple (i.e. non-unique) solutions are shown and we discuss the likelihood of these being genuine, rather than an artefact of the numerical scheme.