In this work, the accuracy of a DtN finite element approach is numerically assessed. This procedure allows an efficient and accurate numerical solution of boundary-value problems of axisymmetric elasticity in semi-infinite domains. For this kind of problems, no explicit closed-form expression for the associated DtN map exists, so a suitable semi-analytical approximation of it, in series form, is used to impose exact boundary conditions on a semi-spherical artificial boundary. The procedure is tested by solving the classical Boussinesq problem, whose exact solution is known analytically. The computed numerical solution is compared to the analytical solution, achieving an excellent agreement between both solutions, both for displacements and stresses. The convergence of the analytical solution to the numerical solution is numerically demonstrated, in terms of artificial boundary location, series truncation order and finite element mesh size.