Hydraulic fracturing technology is one of the most used and efficient methods of oil reservoir stimulation. A way to improve this technology is the consequent pumping of several different fluids containing different concentrations of different proppants (solid spherical particles). This project with Schlumberger, one of the largest international companies in oilfield services, aims at developing a mathematical model describing this technology. The numerical model will predict the fluids’ and proppants’ location is reduced to formulating and solving numerically a different equation. As a result, the pressure distribution in a fracture will be obtained as a function of time. At the first stage, the clear fluids’ motion will be determined. At the second one, the equations describing proppant motion will be coupled with the fluids’ motion equations and solved.