Kirchhoff and Helmholtz showed, that the radiation of sound from a limited source region can be described by enclosing this source region by a control surface - the so-called Kirchhoff surface. Then the sound field inside or outside the surface, where no sources are allowed and the wave operator on the left hand side applies, can be produced as a superposition of monopoles and dipoles on the surface. The theory follows directly from the wave equation. The source strength of monopoles and dipoles on the surface can be calculated if the normal velocity (for monopoles) and the pressure (for dipoles) on the surface are known respectively. A modification of the method allows even to calculate the pressure on the surface based on the normal velocity only. The normal velocity could be given by a FE-simulation of a moving structure for instance. However, the modification to avoid the acoustic pressure on the surface to be known leads to problems, when considering an enclosed volume at its resonant frequencies, which is a major issue of the implementations of their method. The Kirchhoff integral method finds for instance application in Boundary element methods (BEM). A non-zero flow velocity is accounted by considering a moving frame of reference with the outer flow speed, in which the acoustic wave propagation takes place. Repetitive applications of the method can account for obstacles. First the sound field on the surface of the obstacle is calculated and then the obstacle is introduced by adding sources on its surface to cancel the normal velocity on the surface of the obstacle. Variations of the average flow field (speed of sound, density and velocity) can be taken into account by a similar method (e.g. dual reciprocity BEM).