The motion of deformable drops suspended in a linear shear flow at nonzero Reynolds numbers is studied by numerical simulations in two dimensions. It is found that a deformable drop migrates toward the center of the channel in agreement with experimental findings at small Reynolds numbers. However, at relatively high Reynolds numbers $(Re=80)$ and small deformation, the drop migrates to an equilibrium position off the centerline. Suspension of drops at a moderate areal fraction $(\phi =0.44)$ is studied by simulations of 36 drops. The flow is studied as a function of the Reynolds number and a shear thinning behavior is observed. The results for the normal stress difference show oscillations around a mean value at small Reynolds numbers, and it increases as the Reynolds number is raised. Simulations of drops at high areal fraction $(\phi =0.66)$ show that if the Capillary number is kept constant, the effective viscosity does not change in the range of considered Reynolds numbers (0.8–80). The normal stress difference is also a weak function of the Reynolds number. It is also found that similar to flows of granular materials, suspension of drops at finite Reynolds numbers shows the same trend for the density and fluctuation energy distribution across the channel.