We have developed a model using Monte Carlo methods to simulate x-ray mammography. All possible physical processes of interaction of x-rays with matter have been taken into account. A simplified geometry of the mammographic apparatus has been considered along with a software phantom of compressed breast. The phantom may contain inhomogeneities of various compositions and sizes. We have used this model to produce Monte Carlo mammograms under realistic conditions. The validation of the simulation includes both the modelling of physical processes and the production of Monte Carlo mammograms. The first part is accomplished by the demonstration of the coincidence between Monte Carlo and theoretical data, whereas the second is accomplished by the comparison of real mammograms, taken from irradiation of a simplified breast phantom that we have constructed, and Monte Carlo mammograms taken from simulation of the above phantom under the corresponding exposure conditions. The limitations of the model as well as the future use of Monte Carlo mammograms are discussed.