SUMMARY A set of Green's functions is presented for calculating the coseismic strain caused by four independent seismic sources in a spherically symmetric, non-rotating, perfectly elastic, and isotropic (SNREI) earth model. Corresponding expressions are derived assuming that the seismic sources are located at the polar axis. The proper combination of these expressions allows calculation of the coseismic strain components resulting from an arbitrary seismic source at any Earth position. Calculations of strain components are made for the near field resulting from the four independent sources at a depth of 32 km inside the 1066A earth model. Results agree well with those calculated for a half-space earth model, thus confirming the validity of the theory presented in this research. A case study is performed and earth model effects are investigated. Furthermore, this paper investigates effects of spherical curvature and the stratified structure of the Earth in computing coseismic strain changes. Curvature effects are small for three types of seismic sources, but extremely large for the horizontal tensile opening on the vertical fault plane. Because a general coseismic deformation comprises four independent solutions, the large curvature effect on the horizontal tensile opening source contributes to the general result. Effects of Earth's stratified structure are large for all depths and epicentral distances. They reach a discrepancy greater than 30 per cent almost everywhere, and 100 per cent in a very far field. Results show that effects of crustal structure mainly exist in the near field; they do not affect results for a far field.