© 2020 by the authors. The influence of surface bulges and cavities within metals is an important metallurgical-mechanical problem that has not been fully solved and motivates multiple discussions. This is not only related to the generation of interfaces, but also to the distribution of alloying components and elements. In this study, Laplace's equation was used to develop a set of equations to describe these kinds of defects in plates, which arise during the development of metallurgical processes, and this can be used for the prediction of pipeline failures subjected to internal pressure. In addition, the stability conditions of a cavity under an internal pressure are analyzed. The developed method allows to identify the stress state in the generation of the cavity and its propagation. In addition to this, finite element analyses were carried out in order to show first the stress distribution around a cavity subjected to a series of theoretical operation conditions and second to show the crack growth on the tip of the cavity.