In this series of studies, we develop a numerical tool for modeling finite deformation of reservoir rocks. We present an attempt to eliminate the main limitations of idealized methods, for example, elastic or kinematic, that cannot account for the complexity of rock deformation. Our approach is to use rock mechanics experimental data and finite element models (Abaqus). To generate realistic simulations, the present numerical rheology incorporates the dominant documented deformation modes of rocks: (1) rock mechanics experimental observations, including finite strength, inelastic strain hardening, strength dependence on confining pressure, strain-induced dilation, pervasive and localized damage, and local tensile or shear failure without macroscopic disintegration; and (2) field observations, including large deformation, distributed damage, complex fracture networks, and multiple zones of failure. Our analysis starts with an elastic plastic damage rheology that includes pressure-dependent yield criteria, stiffness degradation, and fracturing via a continuum damage approach, using the Abaqus materials library. We then use experimental results for Berea Sandstone in two configurations, four-point beam and dog-bone triaxial, to refine and calibrate the rheology. We find that damage and fracturing patterns generated in the numerical models match the experimental features well, and based on these observations, we define damage fracturing, the fracturing process by damage propagation in a rock with elastic plastic damage rheology. In part 2, we apply this rheology to investigate fracture propagation at the tip of a hydrofracture.