We present results from two-dimensional computer simulations of shearing granular materials, using a molecular dynamics model. We find that there are two distinct modes of deformation of granular materials under shear-"solid-like" characterized by diffuse shear and/or internal shear bands, and "fluidized", characterized by persistent boundary layer shear. Deformation mode is controlled by normal confining stress, system size and velocity, and possibly by other factors like grain shape etc. The velocity pro le is predicted theoretically. The two modes of deformation are characterized by different micromechanical measures, but do not differ in macroscopic measures. The behavior of the weak contacts, and not the stress chains, determine the overall behavior of the system. This has strong implications to stick and slip in granular materials as explained in Sparks and Aharonov, this issue.