A new direct full variational approach is described. The approach exploits a tensor (Kronecker) product construction of the many-electron Hamiltonian and has a number of computational advantages. Explicit assembly and storage of the Hamiltonian matrix is avoided by using the Kronecker product structure to form matrix-vector products directly from the molecular integrals. Computation-intensive integral transformations and formula tapes are unnecessary. The wavefunction is expanded in terms of spin-free primitive kets rather than Slater determinants or configuration state functions and is equivalent to a full configuration interaction expansion. The approach suggests compact storage schemes and algorithms which are naturally suited to parallel and pipelined machines. Sample calculations for small two- and four-electron systems are presented. The preliminary ground state potential energy surface of the hydrogen molecule dimer is computed by the tensor product method using a small basis set. / Ph. D.