This paper presents results obtained from a numerical solution to a stream function–vorticity formulation of the Navier–Stokes equations for the flow around a circular cylinder in planar oscillating flow at small Keulegan–Carpenter numbers (KC) in the subcritical Reynolds number (Re) range. The equations are solved by finite-difference methods. For very small KC ([les ] 1), the numerical results coincide with analytical solutions. As KC is increased, the incipient separation and instability leading to an asymmetrical flow with vortex shedding are predicted. Computed flow fields at small KC values are compared to flow visualizations, and good agreement is found for moderate β-values (≈ 250). The well-documented flow regimes with the transverse vortex street, single-, double- and three-pair shedding, are predicted by the model. Although the flow is not fully resolved for the highest Re values, comparisons of calculated drag and inertia coefficients with experimental data for three different values of the frequency parameter β in the range 196–1035 for 0 < KC < 26 show good agreement.