The current work deals with the simulation of lateral migration of differently shaped particles in a straight channel through which fluid flows with a Poiseuille pattern of flow. The immersed boundary method based on feedback force is adopted for the current work. The equilibrium positions and migration times for circular, elliptical, rectangular, square, and biconcave particles are studied and presented. The cases of neutral and massive (high ratio of particle density to fluid density) particles are presented, and in both scenarios the biconcave particle attains its equilibrium position closest to the bottom wall and the elliptical particle acquires its equilibrium position closest to the channel center. Also, the migration time is highest for the biconcave particle, whereas it is lowest for the rectangular particle.