The complete motion of a solid, rigid, circular cylinder, floating freely in bounded Poiseuille and Couette flow has been calculated at Reynolds numbers between 0 and 10. The results include velocities and forces for cylinders at different positions and sizes. The calculations have been done in an iterative way using a finite element analysis package-FIDAP. The results obtained for the force acting on a cylinder at the center line in Stokes flow agree up to four decimal places with the analytical perturbation solutions at small ratios of cylinder radius to channel width. Stokes solution of the problem shows excellent agreement with the results obtained by Sugihara and Niimi. It has been proved that the Segre-Silberberg effect occurs in the two-dimensional case. The results also show that both the lateral velocity and the equilibrium position are strongly dependent on the cylinder size. Comparison has been made with theoretical and experimental results of the lateral behavior in three-dimensions giving both qualitative similarities and differences.