Acoustic emission sources representing dislocations and cracks under tensile forces, shear forces or a combination of these forces are modelled by a single circular dislocation loop and by a continuous distribution of such loops. The medium is assumed to be linear, elastic isotropic, homogeneous and unbounded. The quasistatic and the point source approximations are assumed. The wave displacement induced by the expansion of a loop and of a continuous distribution of loops is calculated for a tensile and a shear source on the basis of the dynamic dislocation theory by using the Green's function formalism. The wave is given in terms of L-, SV-and SH-waves as a function of the expansion law of the source and is calculated in a simple case. The wave form, radiation pattern and the diameter of the source are calculated; the influence of the expansion time of the source and of the distance between the source and the observation point is discussed. The results are used to check the assumptions of linearity and elasticity. They are compared with experiments and applied to characterise the source from measurements.