A new method of calculating the stress field of an isolated dislocation, or the interaction energy between different dislocations, is presented. While continuum elasticity theory is utilized, account is taken of the finite number of degrees of freedom of real solids through the use of a Debye cutoff in momentum space. As a specific result of this model, it is shown that the stress field of a straight infinitely long dislocation in an elastically isotropic solid varies at large distances $r$ as $\frac{[1\ensuremath{-}{J}_{0}({q}_{D}r)]}{r}$, where ${q}_{D}$ is the Debye radius in $q$ space and ${J}_{0}(z)$ is the zero-order Bessel function of the first kind. Some physical consequences of this perdicted behavior are discussed briefly.