Estimates of the distribution of absorbed dose and dose equivalent with depth in a tissue slab have been made for irradiation by normally incident and also isotropically incident protons and neutrons with energies up to 2.0 GeV. The Monte Carlo calculations, based on a simplified model for nuclear interactions, take into account the production of pions as well as nucleons in nuclear interactions. The energy deposited due to ionization by charged particles is separated into LET ranges permitting different quality factors to be used. The total dose is broken down to show the contribution due to ionization by primary particles (in the case of incident protons), ionization by secondary particles, ionization by pions, excitation of residual nuclei following cascades, and the contribution from pions that stop within the tissue. Results are presented in the form of graphs showing the distribution of absorbed dose and dose equivalent with depth within the phantom for incident energies 0.6, 1.0, and 2.0 GeV. The results appear to be in reasonable agreement with experimental results. There is a rapid buildup of dose near the surface and then a more gradual buildup in the remainder of the 30 cm thick tissue slab. Pions are found to contribute less than 10% of the total dose. For normally incident neutrons, the quality factor decreases from near 10 at the surface from which the neutrons are incident to approximately 2.5 near the back of the slab.