We design and fabricate elastically tunable monodisperse microcapsules using microfluidics and cross-linkable polydimethylsiloxane (PDMS). The overall stiffness of the microcapsules is governed by both the thickness and cross-link ratio of the polymer shell. Flowing suspensions of microcapsules through constricted spaces leads to transient blockage of fluid flow, thus altering the flow behavior. The ability to tune microcapsule mechanical properties enables the design of elastic microcapsules that can be tailored for desired flow behavior in a broad range of applications such as oil recovery, reactor feeding, red blood cell flow and chemical targeted delivery.