A continuum damage mechanics (CDM) based constitutive model has been developed to describe elastic, plastic and damage behavior of rock during drilling. In addition to inelastic deformations, this model incorporates rock anisotropies like toughness anisotropy due to the bedding planes orientation that is a common observation in soft Shales. The pressure sensitive inelastic deformation of porous rocks together with their damage mechanisms are studied for drained and undrained conditions. Fracture mechanics of microcrack and micro-void nucleation and their coalescence are incorporated into the formulation of the CDM models to accurately capture different rock failure modes. The performance of the developed elastoplastic and CDM models are compared with the available single cutter test data of a specific shale play and then the models are introduced into a commercial finite element package through user-defined subroutines. A workflow to derive the required model parameters is presented through inverse modelling of the single cutter test data. The developed CDM model outperforms the traditional discrete element and fracture mechanics approaches by removing stress singularities at the fracture tips and simulation of progressive fractures like formation of the cuttings ribbon without any essential need for remeshing. This model would provide a robust tool for modeling bit performance and rate of penetration using conventional elements of FEA with a reliable results and a computational cost less than similar computational techniques like discrete element methods.