Oxygen concentration plays a key role in cell survival and viability. Besides, it has important effects on essential cellular biological processes such as cell migration, differentiation, proliferation and apoptosis. Therefore, the prediction of the cellular response to the alterations of the oxygen concentration can help significantly in the advances of cell culture research. Here, we present a 3D computational mechanotactic model to simulate all the previously mentioned cell processes under different oxygen concentrations. With this model, three cases have been studied. Starting with mesenchymal stem cells within an extracellular matrix with mechanical properties suitable for its differentiation into osteoblasts, and under different oxygen conditions to evaluate their behavior under normoxia, hypoxia and anoxia. The obtained results, which are consistent with the experimental observations, indicate that cells tend to migrate toward zones with higher oxygen concentration where they accelerate their differentiation and proliferation. This technique can be employed to control cell migration toward fracture zones to accelerate the healing process. Besides, as expected, to avoid cell apoptosis under conditions of anoxia and to avoid the inhibition of the differentiation and proliferation processes under conditions of hypoxia, the state of normoxia should be maintained throughout the entire cell-culture process.