Abstarct: In this project the purpose is to hold forth a new specimen in order to improve standard specimens to achieve better results of applied researches on the behavior of semi-elliptical cracks propagation in thick-walled, high-pressure cylindrical vessels for better adaptation of stress intensity factor changes between specimen and vessel across the direction of crack propagation. In chapter 1 it will begin with an introduction to the fracture mechanics and fatigue behavior of cracks. In chapter 2 we will run on the theoretical researches about under pressure cylindrical vessels also the stress distributions and kinds of possible cracks in vessels will be observed in this chapter. In chapter 3 previous researches and results in the relation with the failure in cylindrical vessels, such as usage of weight functions are expressed. In chapter 4 it is represented that how to find the geometrical properties of the new specimen. And finally in chapter 5 accurate peruses are done to compare the fatigue crack propagation behavior in real cylindrical vessel with new specimen and standard specimen. Also in this chapter the empirical experiments that are done to confirm and validate the computational finite element results are documented and the consequence of comparison is exhibited.