We study the propagation of nucleons and nuclei in tissue-like media within a Monte Carlo Model for Heavy-ion Therapy (MCHIT) based on the GEANT4 toolkit (version 8.2). The model takes into account fragmentation of projectile nuclei and secondary interactions of produced nuclear fragments. Model predictions are validated with available experimental data obtained for water and PMMA phantoms irradiated by monoenergetic carbon-ion beams. The MCHIT model describes well (1) the depth-dose distributions in water and PMMA, (2) the doses measured for fragments of certain charge, (3) the distributions of positron emitting nuclear fragments produced by carbon-ion beams, and (4) the energy spectra of secondary neutrons measured at different angles to the beam direction. Radial dose profiles for primary nuclei and for different projectile fragments are calculated and discussed as possible input for evaluation of biological dose distributions. It is shown that at the periphery of the transverse dose profile close to the Bragg peak the dose from secondary nuclear fragments is comparable to the dose from primary nuclei.