This paper aims to explore the feasibility of providing boundary layer propulsion and flow control by means of embedded aerofoils that are oscillating in the pure plunge mode. To this end, Navier-Stokes calculations of the low-speed flow over a flat plate with an oscillating small foil in close vicinity to the plate were performed to determine the influence of the wall distance, Reynolds number, and reduced frequency on the aerofoil thrust. The simulations were extensively validated against water tunnel experiments at Reynolds numbers between 440 to 5,940. Good agreement was obtained in terms of mean streamwise velocity profiles and the vortical wake patterns. Results indicate that the thrust increases from its value in unbounded flow with decreasing distance from the plate. The propulsive efficiency exhibits a consistent peak at a non-dimensional plunge velocity of about 0.55. For wall distances between one-half to one chord lengths, vortex pairs are shed in a slightly upward deflected direction independent of the starting motion of the aerofoil. As the wall distance increases further, these vortex pairs change into the well-known reverse Karman vortex street. Example calculations for a flat plate with two foils mounted close to the plate trailing edge and oscillating in counterphase confirm the device’s efficacy.