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An understanding of the motion of soft capsules in microchannels is useful for a number applications. This knowledge can be used to develop devices to sort biological cells based on their size and stiffness. For example, cancer cells have a different stiffness from healthy cells and thus can be readily identified. Additionally, devices can be developed to detect flaws in synthetic particles. Using a 3D hybrid lattice Boltzmann and lattice spring method, the motion of rigid and soft capsules in a pressure-driven microfluidic flow was probed. The effect of inertial drift is evaluated in channels different Reynolds numbers. Other system parameters such as capsule elasticity and channel size are also varied to determine their effect. The equilibrium position of capsules in the channel is also obtained. The equilibrium position of rigid and soft capsules depends on the relative particle size. If the capsule is small, the equilibrium position is found to be closer to the channel wall. Conversely, for larger capsules, the equilibrium position is closer to the channel centerline. The capsule stiffness affects the magnitude of the cross-stream drift velocity. For a given Reynolds number, the equilibrium position of softer capsules is closer to the channel centerline. However, It is found that the equilibrium position of soft capsules is insensitive to the magnitude of the Reynolds number.