Hydraulic fracturing is a commonly used method for producing oil and gas from reservoirs. Analysis of hydraulic fracturing requires the study of fracture mechanics and fluids mechanics. The focus of this paper is to investigate the initiation and growth of cracks in a typical well. The finite element method is used to simulate the process of hydraulic fracturing, calculating the effective parameters in fracture analysis and studying the fracture characteristics under different conditions. According to the linear elastic fracture mechanics, if the stress intensity factor is equal to fracture toughness, the crack will propagate. The fracture parameters related to a semi-elliptical crack are studied using the finite element software ANSYS. The numerical results indicate that the stress intensity factor increases by increasing the crack length. The crack length increases by increasing the fluid leakage rate. The relationship between stress intensity factor, leakage rate and crack length (which represents crack growth in each step) is investigated.