Archambeau gave elastic relaxation coefficients for a spherical cavity introduced into a pure shear prestress field. The technique is generalized to a stress field for which only the trace of σ_(ij)^(0) is zero. The coefficients are given for a general deviatoric prestress field of arbitrary orientation. They are then specialized to the case of a pure shear stress expressed in terms of the orientation angles commonly used in fault plane descriptions, i.e. dip and slip angle. The extension of this technique to an arbitrary homogeneous prestress field and its limitations are discussed.