Known for the properties of broadband and circular polarization, spiral antennas have become sufficiently attractive for services of modern and mobile telecommunications. In this work a cavity-backed slot spiral antenna was analyzed. Because of its complex geometry, it was chosen a hybrid numerical method, carried through an implementation of mixing elements of the finite elements - boundary integral method. Based in this formulation, a computer program was developed. A great effort was carried out in order to write the program thus the computational storage and necessities were minimum, good part obtained by application of the boundary conditions on the metallic surface. With the goal of better exploring the geometry of the problem, a mesh of finite elements was defined where the part that fit the aperture was divided into quadrilaterals, while that in the rest of the surface, triangular elements were used. By repeating this mesh along the height of the cavity, hexahedrals and prisms formed the final mesh. For each kind of element, specific vector base functions were applied. In order to verify the accuracy of the algorithm, the same computational program was used in the analysis of a cavity-backed slot rectangular antenna.