This work is concerned with the derivation of general analytical formulae for the matrix elements, in an M representation, of effective two-nucleon interaction. The anisotropic harmonic oscillator wave equation is solved in cylindrical coordinates and the subsequent wave functions used to find the desired matrix element expressions. Since these expressions are in a form conducive to rapid machine computation this representation is well suited for spectroscopic calculations for deformed nuclei. This is illustrated by the calculation of the relative Mng energies, by means of a limited Hartree—Fock method, of several nucleonic configurations in the 2s-ld shell. / Thesis / Master of Science (MS)