The Monte Carlo method is used to model fat cells and the nuclei of stem cells in haemopoietic tissue where 222Rn is dissolved in different amounts in the fat and tissue. Calculations are performed for fat cells of diameters 50 and 100 microns and for stem cell nuclei of 8 and 16 microns diameters for various fractions of fat filling the volume. Average doses (and their distributions) to stem cell nuclei from single passages of alpha particles are presented. In addition to dose, the relationship between LET and dose is obtained, illustrating the importance of 'stoppers' in the calculations. The annual average dose equivalent for a concentration of 1 Bq/m3 in air agrees well with other authors at 12 mu Sv/year. The method also allows the calculation of the fraction of stem cell nuclei hit annually. Here for 1 Bq/m3, stem cell nuclei of diameter 8 microns and 100% fat filing 15 x 10(-7) of the stem cell nuclei are hit.