AbstractOrbital flow past a cylinder is relevant to offshore structures. The numerical scheme presented here is based on a finite‐difference solution of the Navier–Stokes equations. Alternating‐directional‐implicit (ADI) and successive‐over‐relaxation (SOR) techniques are used to solve the vorticity‐transport and stream‐function equations. Theoretical simulations to low Reynolds number flows (up to 1000) are discussed for cases involving uniform flow past stationary and rotating cylinders and orbital flow past a cylinder. The separation points for cylinders that are rotating or immersed in an orbital flow are deduced from velocity profiles through the boundary layer using a hybrid mesh scheme. During the initial development of orbital flow surface vorticity on the impulsively started cylinder dominates the flow. A vortex then detaches from behind the cylinder and establishes the flow pattern of the orbit. After some time a collection of vortices circles the orbit and distorts its shape a great deal. These vortices gradually spiral outward as others detach from the cylinder and join the orbital path.