Distributions of "physical" and "biological" dose in different organs were calculated by coupling the FLUKA MC transport code with a geometrical human phantom inserted into a shielding box of variable shape, thickness and material. While the expression "physical dose" refers to the amount of deposited energy per unit mass (in Gy), "biological dose" was modelled with "Complex Lesions" (CL), clustered DNA strand breaks calculated in a previous work based on "event-by-event" track-structure simulations. The yields of complex lesions per cell and per unit dose were calculated for different radiation types and energies, and integrated into a version of FLUKA modified for this purpose, allowing us to estimate the effects of mixed fields. As an initial test simulation, the phantom was inserted into an aluminium parallelepiped and was isotropically irradiated with 500 MeV protons. Dose distributions were calculated for different values of the shielding thickness. The results were found to be organ-dependent. In most organs, with increasing shielding thickness the contribution of primary protons showed an initial flat region followed by a gradual decrease, whereas secondary particles showed an initial increase followed by a decrease at large thickness values. Secondary particles were found to provide a substantial contribution, especially to the biological dose. In particular, the decrease of their contribution occurred at larger depths than for primary protons. In addition, their contribution to biological dose was generally greater than that of primary protons.