The study of defect problems in real anisotropic crystals is facilitated by using Green Function techniques. The fundamental nature and relevance of the anisotropic elastic Green function is thus introduced in Chapter 1. The chapter also contains a summary of the scope of the thesis. The various representations of the anisotropic elastic Green function are presented and discussed in the second chapter. Expressions for the displacement and related fields of a number of commonly observed defects, together with expressions for the elastic interaction energy between such defects are derived in terms of the Green function in Chapter 3. These expressions are then used to evaluate the interaction energy between an interstitial dislocation loop in copper and a nearby interstitial atom. The Green function and the stress fields of defects observed in alpha-uranium are evaluated in Chapter 5. The various expressions for defect-defect interaction energies are developed in Chapter 6 to provide a new and more precise discussion of the phenomenon of growth in alpha-uranium. In particular, exact expressions for the interaction energy between finite dislocation loops are presented and appropriate numerical evaluation is given. The results obtained show clearly why these elastic interactions play such an important role in separating the population of vacancy and interstitial loops on to different crystallographic planes. This separation in the population and the tendency to form planar rafts of dislocation loops is considerably enhanced by the inclusion of the anisotropy and the finite nature of the loops in the interaction calculation. The Appendices 1 and 2 contain the explicit expressions for the coefficients of the sextic polynomial required in the derivation of the Green function for a body with triclinic symmetry and the coefficients of the double Fourier series representation of the Green function for a-uranium respectively.