In Boundary Element Method analysis, the integration procedure is one of the most important tasks, since one has to deal with singular and quasi-singular integrals which introduce numerical errors in the results, if they are not evaluated adequately. In the last years, several researchers have suggested different techniques with the aim of handling the problem adequately. This work begins presenting some basic concepts and a review of the most important work published before. Following, it introduces a unified integration technique which has a simple form and provides highly accurate results. The proposed scheme also deals with one- or two-dimensional singular or quasi- singular integrals having single or multiple poles. Besides the study of the integrals, a computational code was developed using an objectoriented computer language (C++). This code takes into account the conventional and hybrid formulations of the Boundary Element Method and supports different types of engineering analysis. This computer program was developed in a frame of a joint project with some researchers from the University of Stuttgart.Finally, several numerical examples and analysis results are displayed, showing the good performance of the proposed technique and the influence of the integration task in analysis using Boundary Element Methods.