Different definitions of the reaction matrix G appropriate to the calculation of nuclear structure are reviewed and discussed. Qualitative physical arguments are presented in support of a two-step calculation of the G-matrix for finite nuclei. In the first step the high-energy excitations are included using orthogonalized plane-wave intermediate states, and in the second step the low-energy excitations are added in, using harmonic oscillator intermediate states. Accurate calculations of G-matrix elements for nuclear structure calculations in the A approximately 18 region are performed following this procedure and treating the Pauli exclusion operator Q/sub 2p/ by the method of Tsai and Kuo. The treatment of Q/sub 2p/, the effect of the intermediate-state spectrum and the energy dependence of the reaction matrix are investigated in detail. The present matrix elements are compared with various matrix elements given in the literature. In particular, close argument is obtained with the matrix elements calculated by Kuo and Brown using approximate methods.