For many years, the legal regulations governing radiation protection were primarily concerned with artificial radioactivity, omitting in practice the hazards associated with the occurrence of natural radioactivity in non-nuclear industry. Meanwhile, materials with enhanced concentration of natural isotopes can pose serious radiation risks. A spectacular case is the hazard posed by short-lived radon progeny in underground mine workings. This hazard is significant even when radium isotope concentration in the rocks is at the natural level, and the main reason is relatively poor ventilation of mine workings. The current study contains a description of a developed model that includes a mathematical pattern of the ventilation network and possible radon sources. The model takes into account radon exhalation, generation of radon and its short-lived progeny, losses due to radioactive decay and diffusion of particles and their gravitational deposition; finally, it enables the estimation of doses to miners on the basis of recommended conversion factors. In addition the influence of size distributions of radioactive aerosols on dose conversion factors is discussed. To check and calibrate the model, measurements of radon concentration and potential alpha energy concentration of its decay progeny in an underground hard coal mine were performed during the mining operation.