Abstract：The second algebra system Mathematica is used to deduce analytical solution in some theories of rock engineering in this paper. The method，for example，takes the soil and the pile as a whole system (visco-elastic half-space embedded pile).Using the method of the continuum mechanics，the nonlinear visco-elastic pile-soil mode is established. Assuming that the pile is a Euler beam with circular cross-section，the visco-elastic material and the soil are composed of two parts：an outer infinite linear visco-elastic zone and an inner nonlinear visco-elastic zone (hollow cylinder). In the three-dimensional cylindrical coordinates，the boundary value problem and joining condition are presented. The computer with the system Mathematica goes through the four main processes of symbolic operation，numerical calculation，plotting and programming. The results of this method agree well with Novak¢s results.
