In this work, we analyze the formation of Faraday waves on the free surface of a liquid layer covered by an insoluble surfactant. The linear analysis that is conducted includes the effects of both surface elasticity and surface viscosity. The critical force needed to form the waves, as well as the critical wavenumber, are determined within a large range of values of the dimensionless parameters representing the physicochemical properties of the surfactant. The examination of carefully selected hydrodynamic variables provides further insight into the behavior of the system.