The motion of a rigid cylindrical particle freely suspended in a two‐dimensional channel flow is studied numerically at low Reynolds numbers. The particle is assumed to be an elliptic cylinder or a doublet consisting of two equal‐sized circular cylinders held in rigid contact. The Stokes equations for the suspending fluid are numerically solved with a finite element method for an estimate of the longitudinal, lateral, and angular velocities of the particle at conditions of zero force and zero torque on the particle. Using the velocities obtained, the trajectories of the particle are determined for various initial configurations. The particle is found either to tumble or to oscillate cyclically, depending on the particle size/channel width ratio, particle shapes, and initial conditions. In the former case, both of the elliptic cylinders and doublets rotate continuously in one direction during one period, which is well approximated by so‐called Jeffery’s solutions for a spheroid in unbounded simple shear flow. In the latter case, the particle oscillates in rotation, accompanied by a periodic sidewise drift. The sidewise drift of doublets is about the center plane of the channel, while the mean lateral position of elliptic cylinders is either on or off the center plane.