When a mechanical component present cracks, the determination of the critical size of these cracks, as well as their speed of growth, it is essential in order to assure a reliable operation of the component. The correct estimate of the growth of the crack permit the taking of technical decisions related with the rehabilitation or opportune substitution before a catastrophic failure. Exist several manuals of cracks [1,2] with analytic solutions in order to determine the stress intensity factor of very diverse geometric configurations of cracks and of types of stress. However, most of manual statements consider the cracks in an infinite body or on the surface. In the case of cracks of turbine rotors, they are located near the surface of the central bore, for what they could not be tried neither like superficial cracks neither like cracks buried in an infinite body. In this paper, they come the results of the numeric models of elliptic and tunnel buried cracks near to the surface applying the Finite Element Method. They were carried out several FEM models considering several ligaments between the tip of the crack and the surface. The results of finite element were normalized for later one stablish a polynomial that corresponds to the factor of geometric correction “F” for elliptic cracks buried near the surface. The results obtained with our expression to elliptic cracks, they are compared with the results of Saxena, obtaining a good agreement to the analysis of the grown of the crack of the Gallantin rotor.