In this paper, we discuss the motion of a vesicle in a linear shear flow. It is known that deformable vesicles such as liposomes show the so-called tank-treading and tumbling motions depending on the viscosity ratio between the inside and outside of the vesicle, the swelling ratio, and so on. First, we have conducted numerical simulations on the tank-treading motion of a liposome in a linear shear flow and compared the results with other numerical and experimental results. It is confirmed that the inclination angle of the vesicle becomes smaller when the viscosity ratio becomes larger or the swelling ratio becomes smaller and that the present results show quantitatively good agreement with other results. Then, the effects of membrane modeling are discussed from the mechanics point of view. There are two types of modeling for the lipid bilayer biomembrane. One is a two-dimensional fluid membrane, which reflects the fluidity of the lipid molecules. The other is a hyperelastic membrane, which reflects the stiffness of cytoskeleton structure. Liposome is usually modeled as a fluid membrane and red blood cell (RBC) is modeled as a hyperelastic one. We discuss how these differences of membrane models affect the behaviors of vesicles under the presence of shear flow. It is shown that the hyperelastic membrane model for RBC shows a less inclination angle of tank-treading motion and early transition from tank-treading to tumbling.