In this study, a new approach of the application of finite element method is presented, to solve the initial stages of crack propagation problems which mean the deformation due to the stress and strain of a material. In early applications of the finite element method for the analysis of crack propagation, the crack-tip motion was modelled by discontinuous jumps. We have implemented one dimensional finite element discretization to solve crack propagation problem. The parallel algorithm with parallel computer system has been used in order to perform the computational analysis of finite element for this study. Parallel Virtual Machine (PVM) has been used as a message passing software with Parallel Computer System. The result of this study will be useful in the mathematics and engineering fields. In mathematics, the research will widen the application of finite elements in solving the engineering science problems.