A viscoplastic self consistent model was developed using a rate sensitive constitutive relation, isotropic hardening law, and considering the interaction between the grains and their surroundings. The model was applied to simulate the mesoscopic responses of fcc polycrystalline aggregate during tensile deformation. The macro textures, the grain rotation behaviors, plastic strain and stress heterogeneities, and slip system activities were investigated. The model successfully predicts the typical tensile textures, the grain rotations toward (111) and (100) directions and the orientation dependent slip activities, etc. The simulation results are qualitatively in agreement with experimental measurements and theoretical predictions.