Summary: We present the results of a numerical study of the viscous oscillating flow around a circular cylinder at Reynolds number 200 and Keulegan-Carpenter number 20. The finite element method was used for the solution of the Navier-Stokes equations, with the streamfunction and the vorticity being the field variables. The computation revealed a complicated flow pattern at which the flow is not periodic but switches between different modes in various oscillation cycles. The vortex shedding patterns occurring in different cycles were identified by means of numerical flow visualization. The traces of the hydrodynamic forces were derived from the solution, and the hydrodynamic coefficients of the in-line force were evaluated.