A secondary-dose equivalent model for calculating secondary proton and neutron doses in arbitrary geometries is described. The random position of origin of the secondary-nucleon, primary-proton residual kinetic energy and secondary-nucleon kinetic energy, and survival weight at the point of generation of the secondary particles are determined by random sampling techniques. Results from this model are compared with the experiment of Maienschein and Blosser which measured the dose from a 160-MeV proton be am incident on an aluminum slab. The agreement is generally better than the state-of-the-art accuracy for secondary-dose calculations.