An apparatus for generating focused acoustical pressure waves for therapeutical applications and, in particular, for destroying concrements, corporeal stone, etc., comprises a sound generating unit, which generates pressure waves in a coupling medium, a reflector which focuses the waves and having, if necessary, a locating unit for locating the concrements, corporeal stones, etc., to be destroyed. The sound generating unit is a corpus or body which is axially symmetrical to an axis running through the focal point and whose casing extends in the direction of the axis and is the emission area for the waves. The sound generating unit generates axially symmetrical pressure waves, the propagation direction of which is essentially perpendicular to the axis.