The flow of suspended capsules through small channels sets up a complex problem presented in different applications, from red blood cells on hemodynamics to flow in porous media. The flow of a suspended capsule through a planar constricted channel was analyzed to evaluate the maximum pressure difference necessary to push a capsule through the constriction as a function of its elastic properties, initial tension, dimension, liquid properties, and geometry of the channel. Flow of inner and continuous liquid phases was described using the two-dimensional Navier-Stokes equations and capsule membrane deformation was modeled using a one-dimensional spring-like flexible structure. The fluid-structure interaction problem was solved by coupling finite element and immersed boundary methods. The results reveal the mobility reduction of the flow, associated with the deformation of the suspended capsule as it flows through the constriction, and it can be used to design microcapsules used to block the preferential flow path in the oil-displacement process in porous media.