In this work, we consider a mathematical model of viscoelastic incompressible fluid governed by the Navier-Stokes-Voigt equations in a three dimensional thin domain Ω ε , with damping term and Tresca friction law. First, we give the problem statement and the weak variational formulation of the considered problem. Then we study the asymptotic analysis of the problem when a dimension of the domain tends to zero. The limit problem and the specific equation of Reynolds are obtained.