The energy density εg of asymptotically flat gravitational fields can be calculated from a simple expression involving the trace of the torsion tensor. The integral of this energy density over the whole space yields the Arnowitt–Deser–Misner (ADM) energy. Such energy expression can be justified within the framework of the teleparallel equivalent of general relativity, which is an alternative geometrical formulation of Einstein’s general relativity. In this paper we apply εg to the evaluation of the energy per unit length of a class of conical defects of topological nature, which include disclinations and dislocations (in the terminology of crystallography). Disclinations correspond to cosmic strings, and for a space–time endowed with only such a defect the well known expression of energy per unit length is obtained precisely. However for a pure space–time dislocation the total gravitational energy is zero.