The objective of this study is to develop a model for the grinding process for predicting the temperature, thermal stress and thermal deformation. The thermal load during grinding is modeled as uniformly distributed, 2D heat source moving across the surface of elastic half space, which is insulated or subjected to convective cooling. That non-dimensional temperature distribution, non-dimensional longitudinal stress distribution and non-dimensional thermal deformation distribution are calculated with non-dimensional heat source half width and non-dimensional heat transfer coefficient. Finite element models are developed to simulate moving heat source, which is modeled as uniformly or triangularly distributed, the FEM simulation is compared with numerical solution.