A Monte Carlo transport code for calculating high-energy nucleon-meson cascades in thick targets is described. The calculational method uses an intra-nuclear-cascade-extrapolation-evaporation model for treating nonelastic collisions ≳3 GeV. Calculated results for the development of the cascade induced in thick iron targets by 10-, 19.2-, 29.4-, and 200-GeV/c protons are presented. For the cases of 10-, 19.2-, and 29.4-GeV/c incident protons, comparisons are made with experimental data and, in general, good agreement is obtained.