Stem cell is becoming an important cell source in now emerging fields such as tissue engineering, regenerative medicine or cell therapy. They are characterized by two properties: multipotency and self-renewal ability. Satellite cells, from skeletal muscle, are able of self-renewal but are committed to muscle phenotype. Nonetheless, it is now recognized their important role in muscle regeneration. Their progeny, myoblasts, fuse to form multinucleated myotubes sharing their nuclei, this feature suggests satellite cells as a powerful vector for gene transfer. However, their therapeutic use will require a means to expand the cell population, from a biopsy, in vitro. We developed a mathematical model that aims to be a starting point to describe and predict the expansion of a satellite cell culture. It has a population balance (PBE) form, which is a powerful means to describe synthetically a population made of thousands of cells, even if cellular phenomena are deterministically defined at the single cell level. The cell cycle kinetics is modeled taking into account cell death and contact inhibition due to cell-cell signaling. Model parameters are adjusted to experimental data, consisting of cytometric analyses and cell number density measurements by a Coulter counter, at different time points. Experimentally, satellite stem cells, isolated by single muscle fibers of adult rat, are seeded at different initial cell concentrations on Petri dishes and cultured under static conditions. Model outcome is in accordance with the experimental data and a sensitivity analysis is performed to highlight the importance of single model parameters. Moreover, the temporal evolution of cell number densities for each cell generation is simulated. Tracking the percentage of cells in each generation is important to obtain the experimental condition that minimizes telomere shortening, which depresses stem cells myogenic potential.