The flow patterns around and the forces acting on an oscillating bluff body submerged in a fluid at rest have been studied by numerical simulations. An ALE (Arbitrary Lagrangian-Eulerian) finite difference method has been employed to simulate the flow around an oscillating bluff body, e.g., a circular cylinder and a square one, submerged in a still water. Simulations have been carried out under the assumption of 2- and 3-dimensional, unsteady, incompressible and viscous flow. The results predicted by numerical simulations are compared with our recent results of measurements of fluiddynamic forces on and flow-visualized patterns around a bluff body that is set in a planar oscillatory flow generated by a U-tube water tank up to Keulegan Carpenter (KC) numbers of 30 and at a value of β of 95 and 153. Although flow-patterns around a bluff body are complicatedly produced by both the vortex-shedding from a bluff body and the planar oscillatory flow, the major vortex-shedding regimes observed in experiments, flow pattern of “3-dimensional structures” at low KC numbers, “transverse street” and “double pair” all can be successfully reproduced in the present simulations, and there is good agreement between the simulated and measured flow patterns. Notable differences are also confirmed for flow configurations around a bluff body with a different shaped-section, e.g., a circular section and a square one. There is found to be good agreement also between the predicted and measured in-line forces, i.e., the values of drag and inertia coefficients, CD, CM, represented by the well-known Morison’s equation and the fluctuating transverse force (lift force) CL across a range of KC values. Furthermore, it is noteworthy that the values of transverse force depending on KC numbers correspond well to the process of flow pattern variation.