This work is related to the study of discontinuity stresses in pressure vessels, more specifically to the case of a circular plate pressure vessel. It presents a comparative study between a discontinuity stresses analytical model and a finite element numeric model using a simulation software (ANSYS). The study includes also comparisons of different investigative analyses using this software in order to define the best model for solving the case. Initially, the discontinuity stresses were computed by the analytical model using the MatCad calculation software. The discontinuity equations allowed us to compute the circunferential and longitudinal principal stresses, exactly at the aimed spot in the discontinuity region. The difference between the employed numeric models is related to their element of analysis considering the following: the shell elements, the solid elements and the axisymmetrical elements. For each one of these models was choosen an specific mesh, and for the axisymmetric model were choosen two different element sizes for comparison purposes. After computing the analytical and numeric models we were able to compare the results and arrive to the study conclusions. It was found out that different numeric models present similar results but their differences are more significative when the element sizes were varied. Moreover, the numeric results differ somehow in relation to the analytical results but this do not impede to achieve a coherent result.