Deformation of a red blood cell (RBC) in bounded two-dimensional Poiseuille flows is studied by using an immersed boundary method (IBM). An elastic spring model is applied to simulate the skeleton structure of a RBC membrane. As a benchmarking test, the dynamical behavior of a single RBC under a simple shear flow has been validated. Then we focus on investigating the motion and the deformation of a single RBC in Poiseuille flows by varying the swelling ratio (s*), the initial angle of the long axis of the cell at the centerline (ϕ), the maximum velocity at the centerline of fluid flow (umax), the membrane bending stiffness of a RBC (kb), and the height of the microchannel (H). Two motions of oscillation and vacillating breathing (swing) of a RBC are observed in both narrow and wide channels. The strength of the vacillating-breathing motion depends on the degree of confinement and the value of umax. A RBC exhibits a strong vacillating-breathing motion as the degree of confinement is larger or the value of umax is higher. For the same degree of confinement, the vacillating-breathing motion appears to be relatively weaker but persists longer as the value of umax is lower. The continuation of shape change from the slippery to the parachute by varying the value of umax is obtained for the biconcave shape cell in a narrower channel. In particular, parachute shape and bulletlike shape, depending on the angle ϕ, coexist for the elliptic shape cell given initially with lower umax in a narrower channel.