We consider a scheme of aging with two possible mechanisms of senescence processes: aging with apoptosis and necrosis for differentiated cells and a multistage process of malignant transformation. Our model describes the multistage phenomena of aging and carcinogenesis by a set of stochastic equations using multivariate and diffusion processes. This model fits experimental data on the acceleration of aging processes from postnatal exposure to 5-bromodeoxyuridine (BrdU), and the induction of genome instability. The methods of stochastic modeling and computer simulation of the processes of aging and carcinogenesis have been used for the verification of the biological suggestions.