Crack propagation in materials can lead to catastrophic failures. The understanding of crack propagation in materials is of crucial importance in many industries, including nuclear, chemical and aeronautical applications. From an engineering point of view, fracture mechanics is used as a basis for predicting critical crack size, strength of a structure as a function of crack size, inspection requirements pertaining to size of an admissible crack and the period of time between inspections. It is usually required to determine the distribution of stresses and strains in a body that is subjected to external loads or displacements. The closed form solutions for crack propagation are rarely available. A numerical simulation of such problems is therefore required. This research work uses Finite Element Method (FEM) for Linear Elastic Fracture Mechanics (LEFM) to predict Stress Intensity Factor (SIF) for different crack geometries. The validation of the results based on modeling and simulation is carried out through comparison with our experimental investigations for crack propagation using photo-elastic methods.