To achieve high performance machining, modeling of the cutting process is necessary to predict cutting forces, residual stresses, tool wear, and burr formation. A major difficulty in the modeling of the cutting process is the description of the material constitutive law to reflect the severe plastic deformation encountered in the primary and the secondary deformation zones under high strains, strain rates, and temperatures. A critical literature review shows that the available methods to identify the material constitutive equation for the cutting process may lead to significant errors due to their limitations. To overcome these limitations, a novel methodology is developed in this study. Through conceptual considerations and finite element simulations, the characteristics of the stress, strain, strain rate, and temperature fields in the primary shear zone were established. Using this information and applying the principles of the theory of plasticity, heat transfer, and mechanics of the orthogonal metal cutting, a new distributed primary zone deformation model is developed to describe the distributions of the effective stress, effective strain, effective strain rate, and temperature in the primary shear zone. This analytical model is assessed by comparing its predictions with finite element simulation results under a wide range of cutting conditions using different materials. Experimental validation of this model will be presented in Part II of this study.