A new model describing the reaction stresses during plastic deformation of metals is proposed in which the reaction stresses among the grains and their accumulation are calculated. The model could overcome the shortages of the Sachs and Taylor deformation model. According to the model, the plastic strain tensor induced by activation of slip systems will produce certain elastic reaction stress in the surrounding matrix, which influences the choice of further activation of slip systems as well as the orientation evolution. The model gives more attention to both of the stress and strain compatibility among the grains. The simulation on the tensile deformation of pure copper indicates that the model could exhibit the main characteristics of the real deformation process.