Based on the finite deformation theory of continuum mechanics, the velocity, Eulerian strain, Eulerian strain rate, and deformation rate distributions along a family of assumed streamlines are analytically obtained for an orthogonal cutting operation. An iterative incremental method is used to predict the temperature on the shear plane. The total power in orthogonal cutting may be expressed in terms of three parameters, which are predicted by minimization of the total power. This model allows a general form for the material constitutive equation, which, in general, is a function of strain, strain rate, and temperature. The rotation effect of streamlines on the strain and strain rate calculations is automatically considered using the finite deformation theory of continuum mechanics. In Part I of this paper, the theoretical underpinning for the orthogonal cutting model is established. The verification of the model, including determination of the material constitutive equation using the Hopkinson bar technique, is presented in Part II of this paper.