A Monte Carlo tool which permits the simulation of screening mammography programmes is developed. Various statistical distributions describing different parameters involved in the problem are used: the characteristics of the population under study, a tumour growth model and a model for tumour detection based on parameters such as sensitivity and specificity which depends on the woman's age. We reproduce results of different actual programmes. The model enables us to find out the configuration (the age of the women who attend the screening trials and screening frequency) which produces maximum benefits with minimum risks. In addition, the model has permitted us to validate some of the assumed hypothesis, such as the probability distribution of the tumour detection as a function of the tumour size, the frequency of the histological types and the transition probability between different histological types.