The hybrid boundary element method was introduced in 1987. Since then, the method has been applied successfully to different problems of elasticity and potential, including time-dependent problems. However, some important aspects of the method have remained open to investigation. This dissertation consists in a threefold contribution, with developments outlined for elasticity, but readily extensible to potential problems. The first step is aimed at improving the expression of displacement results in the domain by taking correctly into account the amount of rigid body movements. Based on the assessment of displacements, a simplified formulation of the method is proposed, in which a flexibility-like matrix is directly obtained, in a procedure that requires no integration at all. This novel formulation, as shown in the numerical examples, is extremely accurate and rather inexpensive. Since it lacks a variational basis, however, the method leads to a non-symmetric stiffness matrix. In a third step, both hybrid and simplified boundary element methods are extended to general problems in an infinite domain, for any type of boundary conditions. It is shown that the matrices of both methods are spectrally interrelated. A large number of numerical results of two-dimensional problems validate the theoretical achievements.