The flow inside a square cavity, generated by a uniform oscillatory motion of the upper cavity wall, is investigated. Numerical solutions of the full unsteady Navier–Stokes equations are computed for a selection of Reynolds’ numbers and frequency parameters in the range 0–600. These results show that the steady streaming component of the flow, in general, comprises two main, equal, contrarotating eddies, situated in the upper half of the cavity (one on either side of the cavity centreline) and two weaker, equal, contrarotating eddies, situated in the lower section of the cavity (again one on either side of the cavity centreline).