This work is dedicated to the numerical simulation of two-phase flow (gas/liquid) stratified between two parallel planes and inclined relative to the horizontal. In this context, we have chosen to use a code for solving both the Navier-Stokes equations and the constitutive equations of viscoelastic fluid with finite volume (Gilflow) corresponding to a single phase flow of viscoelastic fluid confined between two horizontal plane walls. The two-phase flow model was here implemented successfully, by application of the quotVolume of Fluidquot method (VOF). The transport of the interface is solved by using the transport equation of the VOF function. Both methods: Hirt-VOF and PLIC-VOF are tested for a two-phase flow in an unsteady stratified flow regime (gas/liquid). To illustrate this numerical simulation, the configuration (gas / liquid) stratified is here presented.