In this paper, the fluid flow and the diaphragm deflection are studied in the pneumatically actuated diaphragm microvalve by performing finite element and analytical fluid-structure interaction simulations. The results of these approaches are compared and their validity is discussed. An analytical relation is obtained for the critical diaphragm deflection which leads to unstable response of the microvalve. This relation shows that the critical deflection is only a function of the microvalve geometry, namely its inlet height and outlet radius. The phenomenon of the diaphragm deflection jump is justified in the microvalve behavior. The effect of different fluid flow and diaphragm parameters on the microvalve response is investigated that can be used to improve the microvalve design.