A formalism is presented for the distorted wave approximation for the inelastic scattering of nucleons by nuclei at intermediate energies which leads to the continuous excited states of the residual nucleus. On the assumption of semi-classical approximation for the distorted waves of the incoming and outgoing particles, the Thomas-Fermi model for the nucleus and the short range of the interaction, the cross section is obtained in a closed form as the sum of local collisions at all the points within the nucleus, which are given by the two nucleon cross sections averaged over the momentum distribution of the target nucleons multiplied by the penetrating and the escaping probability of the incident and the emitted particle, respectively. The localization of the collision is shown to be due to the average procedure over the final states of the nucleus. The semi-classical method of approximation for the distorted wave in the complex distorting potential is successfully carried out by generalizing the “geometrical optics” approximation for a real distorting potential. The resulting expression permits a very simple, intuitive interpretation. Several discussions are given on the validity of the approximation used in the derivation.