A study is made of the effects on the fluid motion past a semi-infinite flat plate of introducing a uniform injection of extra fluid from a finite porous section of the plate. Steady laminar flow is considered with a uniform oncoming stream parallel to the plate in an incompressible fluid. A local analysis valid near the start and finish of the injection is found to produce unusually firm predictions for the singular behaviour of the solution of the Navier-Stokes equations there and in particular shows that separation ahead of the injection is inevitable for all positive Reynolds numbers R. Then a numerical treatment of these singular points, and of the Navier-Stokes equations and boundary conditions, is described and the results are presented for a range of values of R, The calculation method used is based on the accurate and efficient centred differencing technique suggested by Dennis I1] and developed recently by Dennis and Hudson [2]. Checks on the influences of mesh spacing, of the placing for the outer boundaries of the computational domain, and of the treatments of the singular points are given. The agreement found with the previous local analysis near the ends of the injection proves especially encouraging. In addition the results provide some guidance to the asymptotic structure of the flow at high Reynolds numbers and to the questions surrounding the occurrence of large-scale separations.