Deformation of two-dimensional red blood cell in linear shear flow is simulated using the immersed boundary method, in which the cell is modeled as a force source instead of a real body. The effect of three constitutive laws, i.e. Hookean, Neo-Hookean and Skalak elasticity, on the deformation is studied by simulating the cell movement in two linear shear flows. The results show that the effect of the constitutive laws gets more obvious as the shear rate increases. Both the aspect ratio and the inclination of the steady shapes get bigger, and the differences between the periods of the cell tank-treading motion become larger. For the same shear flow, the period with Hookean elasticity is less than the period with Neo-Hookean elasticity and bigger than the period with Skalak elasticity.