This paper presents a computational model that describes the growth of the bone as a function of the proliferation and hypertrophy of chondrocytes in the growth plate. We have included the effects of the mechanical loads on the sizes of the proliferative and hypertrophic areas, the number of proliferative chondrocytes and the final size of the hypertrophic chondrocytes. The validation of the model was performed with experimental data published on other investigations about proximal tibia of rats, subjected to sustained axial stresses of 0.1 MPa, 0.0 MPa, -0.1 MPa and -0.2 MPa. Growth was simulated during 23 days, obtaining numerical errors between 2.77% and 3.73% with respect to experimental growth rates. The results obtained show that the model adequately simulates the behavior of the growth plate and the effect of mechanical loads over its cellular activity.