Failure analysis of thin walled pressure vessels are studied for two different steel materials. Three dimensional Finite Element Models are developed by using Ansys finite element program. Nonlinear static analysis is performed for different pressure and temperature. At first, pressure dependent behavior of pressure vessels are obtained. Then, temperature dependent analysis is simulated. Finally both pressure and temperature dependent behavior is studied. The resultants are used for failure analysis of pressure vessels. The burst pressures are found by using Maximum Stress Criteria and critical failure points are obtained. The failure resultants are compared with Von Mises Stress Criteria results.