We present an approximate (perturbation) method for computing surface displacement fields due to quasi-static dislocations in inhomogeneous elastic half-spaces, extending the work of Du et al. [1994> to three dimensions. Three dimensional methods are required to model geodetic observations. The perturbation method allows one to include more realistic earth structure in the analysis of surface deformation measurements, and is computationally efficient enough to be used in inversions for source properties. As an example, we investigate the effect of material inhomogeneity on the location of the fault plane for the 1989 Kalapana, Hawaii, earthquake. Inversion of coseismic elevation changes assuming a homogeneous half-space yielded a finite source depth markedly shallower than the mainshock and principal aftershocks [¿rnad¿ttir et al., 1991>. Incorporation of lateral and vertical variations in shear modulus, consistent with velocity and density data, yields a source depth more consistent with the seismic results. Failure to account for variations in elastic properties can bias estimates of source depth and moment.¿ 1997 American Geophysical Union