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There is an emerging class of microfluidic bioreactors which possess long-term, closed circuit perfusion under sterile conditions with in vivo-like flow parameters. Integrated into microfluidics, peristaltic-like pneumatically actuated displacement micropumps are able to meet these requirements. We present both a theoretical and experimental characterization of such pumps. In order to examine volume flow rate, we have developed a mathematical model describing membrane motion under external pressure. The viscoelasticity of the membrane and hydrodynamic resistance of the microfluidic channel have been taken into account. Unlike other models, the developed model includes only the physical parameters of the pump and allows the estimation of their impact on the resulting flow. The model has been validated experimentally.