The unilateral buckling of a stressed thin film on a substrate has been investigated theoretically in the framework of the Föppl-von Kármán theory of thin plates when an increasing overpressure is considered onto the upper free surface of the film. It is found that, depending on the initial stress in the film and overpressure, two scenarios of evolution may occur. The snap-through of the one-dimensional buckle leading to the full redeposition should take place for low values of the initial stress. When the initial stress exceeds a critical value, a partial redeposition of the buckle should proceed as the overpressure increases. A snap-through while the redeposition mechanism has taken place should also occur for higher values of the overpressure.