This article investigates the motion of a cell in a carrier fluid flowing along a twodimensional channel. The cell, assumed elliptical, is modeled as a highly viscous fluid with rigid body motion. A fixed grid approach is used. A combined formulation with one set of governing equations to treat both phases is employed. The cell-fluid interface is tracked by a distance function. The finite volume method is employed to solve the governing equations. For demonstration purpose, the result for the flow of a single elliptical cell in an obstructed channel is presented.