When a red blood cell (RBC) is subjected to an external flow, it is deformed by the hydrodynamic forces acting on its membrane. The resulting elastic tensions in the membrane play a key role in mechanotransduction and govern its rupture in the case of hemolysis. In this study, we analyze the motion and deformation of an RBC in a simple shear flow and the resulting elastic tensions on the membrane. The large deformation of the red blood cell is modelled by coupling a finite element method to solve the membrane mechanics and a boundary element method to solve the flows of the internal and external liquids. Depending on the capillary number Ca, ratio of the viscous to elastic forces, we observe three kinds of RBC motion: tumbling at low Ca, swinging at larger Ca, and breathing at the transitions. In the swinging regime, the region of the high principal tensions periodically oscillates, whereas that of the high isotropic tensions is almost unchanged. Due to the strain-hardening property of the membrane, the deformation is limited but the membrane tension increases monotonically with the capillary number. We have quantitatively compared our numerical results with former experimental results. It indicates that a membrane isotropic tension O ( 10 − 6 N/m) is high enough for molecular release from RBCs and that the typical maximum membrane principal tension for haemolysis would be O ( 10 − 4 N/m). These findings are useful to clarify not only the membrane rupture but also the mechanotransduction of RBCs.