Experimental radiobiological investigations of fast neutron beams involve irradiation of thin cell layers. The irradiation of cells is done either in free air or with a material such as graphite, TE plastic or bone-equivalent plastic covering the cells. This paper discusses the computed dose distributions in LET at shallow depths between 5 or 10 micrometers and the equilibrium depth, and the influence of the overlying materials on the distributions. The secondaries considered are elastic recoils of H, C, N and O, and 22 alpha particle groups and the corresponding heavy recoils arising from (n, alpha) events in C, N, O, P and Ca. Dose-average LET and curves of detailed dose distributions in LET as a function of depth in tissue are given for various overlying materials.