This chapter explains the case of Stokes flows, and the case where internal and external fluid inertia is taken into account. It shows that indicators of the capsule relaxation after the step can be predicted by reduced models of the inertial Kelvin–Voigt type. Understanding the flow dynamics of microcapsules in a confined environment and being able to determine and control the mechanical properties of the membrane are of great importance in the context of encapsulation and controlled release of active agents. Gires et al. studied the flow of microcapsules through a microfluidic channel with a step and a cross-section that suddenly changed from square to rectangular. The chapter presents the fundamentals of the immersed boundary method (IBM). The IBM is designed to couple a Cartesian mesh to a Lagrangian mesh. The dynamics of relaxation in the Navier–Stokes regime are better understood if one looks at energy exchanges.