Bone regeneration is a common biological process occurring, for example, during fracture healing or osseo-integration of prostheses. Computer simulation of bone regeneration is difficult to carry out because it is a complex sequence of cell-mediated processes regulated by mechanobiological stimuli. An algorithm to predict the time-course of intramembranous and endochondral ossification has been developed. The algorithm assumes that there are precursor cells in the undifferentiated tissue and that these cells differentiate into either fibroblasts (to form fibrous connective tissue), chondrocytes (to form cartilaginous tissue) or osteoblasts (to form bone), based on a combination of biophysical stimuli derived from strain in the collagenous matrix and flow of the interstitial fluid. Both these stimuli are known to deform the precursor cells, and the authors hypothesise that this causes activation of cell differentiation pathways. The observation that precursor cells take time to spread throughout the fracture callus has been included in the algorithm. The algorithm was tested in an investigation of the fracture healing of a long bone using an axisymmetric finite element model. The spatio-temporal sequence of tissue phenotypes that appear in the course of fracture healing was successfully simulated. Furthermore, the origin of the precursor cells (either surrounding muscle, bone marrow or periosteum) was predicted to have a fundamental effect on the healing pattern and on the rate of reduction of the interfragmentary strain (IFS). The initial IFS=0.15 drops to 0.01 within seven iterations if cells originated from the surrounding soft tissue, but took more than 50% longer if cells originated in the inner cambium layer of the periosteum, and four times longer if precursor cells originated from the bone marrow only.