Abstract - When a red blood cell (RBC) is driven by a pressure gradient through a microfluidic channel, its passage or blockage provides a measure of the rigidity of the cell. This has also been developed as a means to separate RBCs according to their mechanical properties, which are known to change with pathological conditions such as malaria infection. In this study, we use numerical simulations to establish a quantitative connection between the minimum pressure needed to drive an RBC through a contracting microfluidic channel and the rigidity of the cell membrane. This provides the basis for designing such devices and interpreting the experimental data.