Abstract: Aim To determine the relationship between stress and displacement outside the contact domain. Methods\ The Laplace transform and the double Fourier transform were used to study the solution in the transform domain. Some improved algorithms of the Laplace inversion procedure were used to prove all the calculations for different contact regions and materials to be stable. Results and Conclusion\ An analytic solution to three dimensional problem of transient contact dynamics is developed. Based on the solution, contact displacements outside the elliptic contact domain can be determined analytically when the given contact stress is some quite general functions. The correctness of the theorem is also examined by numerical computations for several typical materials and different geometrical characters of the contact domain.