The flow structure and loading due to rectilinear oscillations of a circular cylinder in a steady uniform flow are investigated numerically at a fixed Reynolds number R = 855. Numerical results are obtained over broad ranges of two externally specified parameters, i.e. the frequency of forced oscillation f relative to the natural vortex-shedding frequency f 0 (0.5 ≤ f / f 0 ≤ 4.0) and the angle of inclination η between oscillation axis and free-stream (η = 30°, 45°, 60°, 75°). The dimensionless oscillation amplitude is fixed at A = 0.26. The method of solution is based on the use of truncated Fourier series representations for the stream function and vorticity in the angular polar coordinate. The N avierStokes equations are solved by using finite difference methods, but with the boundary vorticity calculated using integral conditions rather than local finite-difference approximations.