Aim of this work is the application of the hybrid boundary element method to problems of the linear elastic fracture mechanics. Several formulations are introduced and the most relevant aspects of computational implementation are discussed. The mechanical consistency of the hybrid boundary element method enables the adequate mathematical description of the stress field related to a cracked continuum. The main attempt of this dissertation is to develop a computationally simples and fast procedure for the determination of stress intensity factors in two- dimensional elasticity. The effects of opening and sliding of the crack surfaces are considered by means of a hipersingular stress function, which are dealt with adequately in the frame of the variational formulation. It is shown that the stress series proposed by Williams for the local field around a crack tip may be considered as a Green´s function. As a consequence, the stress intensity factors corresponding to both Modes I and II are obtained as primary unknowns of the problem. Several numerical examples are presented in order top validate the formulations proposed. This shows the potentiality of the hybrid boundary element method for dealing with problems of the fracture mechanics.