Most of the wind instruments have side holes that enable to the musician to select a note to play. The modeling of the acoustic radiation of the side holes is commonly approached by an equivalent open tube corrected in length. In practice, instrument makers are required to complete the geometry of a hole with the addition of a chimney whose base can be undercut to ensure a satisfactory functioning of the instrument. The purpose of this work is to study the influence of the side holes geometry on the resonances and the acoustic radiation of a cylindrical resonator. For this purpose, a fast multipole method is used to model the three-dimensional acoustic propagation through side holes of complex geometries. This work first consists in revisiting the literature models by comparing them with different realistic geometries of side holes. The ability to model a 3D pressure field will also be used to derive behavioural laws describing the influence of side hole geometry on the radiated acoustic power.