For samples exposed in high neutron flux regions of reactors the contribution to the total dosage due to the recoils from elastically scattered fast neutrons may be significant. The calculation of this contribution is considered here. Three methods are presented, each differing in the manner in which the details of the energy distribution of fast neutrons are treated. In the first, the neutron flux per unit energy interval is assumed to be of the asymptotic or 1/E form up to fission energies. In the second and third, a separate computation is made for the uncollided neutrons reaching the sample. The remaining contribution due to once-scattered neutrons is treated as in the first method, but alternate forms for the source spectrum of once-scattered neutrons are considered. Use of the equations requires only a knowledge of the thermal neutron flux in the vicinity of the sample. Assumptions and limitations are discussed. Numerical results are presented for comparison of the effects in light water, heavy water, and graphite moderated reactors in the irradiation of a hydrocarbon (cyclohexane) sample.