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In the dislocation theory of a spherical earth model (Sun et al. 1996), the numerical computation of surface deformation caused by an earthquake (also named dislocation) is quite time-consuming. As an approximation of surface deformation, Sun (2004) proposed an analytical asymptotic expression, which has no need of numerical integration of differential equations and summations of infinite Legendre series. In theory, the asymptotic solutions have mathematical simplicity and physical completeness since they reflect earth's curvature and radial structure; and in practical applications, applying of asymptotic solutions can simplify the calculation process, especially for deformations in near-field of shallow earthquakes. However, asymptotic expressions of the surface strain have not been given, and the applicability of the asymptotic theory has not been proved yet. As a supplement and also an application of previous pioneering work (Okub0 1988; Okubo1993; Sun 2004a), in this study we will: 1) apply the expressions of static displacement caused by 4independent point dislocation and give the corresponding asymptotic solutions for strain tensor on earth surface, 2) validate the results with specific results from numerical integrations in spherical earth model.