When a circular cylinder is transversely set in fluid flows, various kinds of oscillations in the in-line as well as the cross-flow direction occur due to the aerodynamic forces, which are mainly induced by periodic vortex sheadings. In case of large amplitude, an oscillating cylinder interacts with flows close to the cylinder surface and generates the distinct vortex shedding patterns. We numerically simulate the aeroelastic behaviors of a circular cylinder. Namely, a cylinder is elastically mounted for both in-line (x) and cross-flow (y) directions, therefore can translationally oscillate in any direction in uniform flows. We examine the aeroelastic characteristics in the in-line and the cross-flow vortex-induced oscillations, and relations among different types of modal motions of a circular cylinder with two degrees of freedom. It is shown that, with regard to the response characteristics, computational results based on three-dimensional simulations agree with the experimental results. In order to clarify the mechanism of the vortex-induced oscillation, we also investigate flow structures under oscillation, for example, the behaviors of separated layers from the cylinder and their following process of vortex formation in the near wake.