  In this paper we present a treatment of hypersingular integral equations,
which have relevant applications in many problems of wave dynamics, elasticity
and fluid mechanics with mixed boundary conditions. The main goal of the
present work is the development of an efficient direct numerical collocation
method. The paper is completed with two examples taken from crack theory and
acoustics: the study of a single crack in a linear isotropic elastic medium,
and diffraction of a plane acoustic wave by a thin rigid screen.
