In this work I numerically investigate the conditions for the onset of a two-dimensional wave motion on the free surface of a horizontal thin liquid layer subject to a vertical periodic acceleration of very small amplitude and very high frequency. The complete set of governing equations (Navier-Stokes and continuity equations) and boundary conditions are solved using the Galerkin/finite element method. The influence of the initial condition, the amplitude of the external acceleration, and the physicochemical properties of the system is analyzed. The time evolution of free surface shapes, velocity fields, and kinetic and surface energies is reported.