Publisher Summary This chapter analyzes with the help of extended immersed boundary method, passing of a simulated cell through a constricted channel. The chapter examines the large deformation of the structure and the stress profile along with instantaneous velocity and pressure distributions. The flow in the stenotic vessel has motivated much of the research in recent decades because of its physiological importance. When a red cell passes through a stenotic vessel, it could be subjected to a significant shear force and forced to squeeze through the stenosis. The extended immersed boundary method in comparison with the traditional CFD/FEM and the immersed boundary method bear the following significant advantages: (1) the finite element representation enables more appropriate and accurate stress analysis than the fiber network representation of the submerged structure, and (2) with EIBM—on a regular fluid grid—the cell passing through a stenotic vessel, can be efficiently stimulated where large deformation and stress distribution are predicted as well as the pressure and velocity profiles of the viscous fluid inside the channel.