Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we propose an asymptotic method of obtaining the solution and means of resolving the singularities and shock waves. This method is implemented as Maple code.