The finite element method has been demonstrated to provide an effective means for the analysis of two-dimensional elastic continua. In this paper, the method is applied to a special class of two-dimensional system: The axially symmetric elastic solid. The procedure is identical with that used in plane stress analysis; it is merely necessary to develop special stiffness matrices for the axi-symmetric finite element. In the present development, axi-symmetric elements of triangular cross section are considered (forming complete rings in plan view). The procedure for evaluating the element stiffness is summarized, and the modifications required to adapt a finite element plane stress digital computer program for the treatment of axi-symmetric systems are cited. Results of several example analyses are presented; the solution of the Boussinesq problem, a concentrated load applied to an elastic half-space, demonstrates the accuracy of results that may be obtained.