The elastic effects of an insoluble surfactant on the formation and evolution of two-dimensional Faraday waves is investigated numerically. We analyse the influence of the elasticity of the surface-active agent on the amplitude of the vertical vibration needed to excite two-dimensional standing waves on the free surface. The numerical solutions show that the interface is always subharmonically excited at the onset and that the presence of the surfactant requires a higher external force to induce standing waves. They also show that the magnitude of the external amplitude is related to the temporal phase shift that exists between the evolution of the surfactant concentration and the free-surface shape. A detailed description of the time-varying velocity fields and interfacial distribution of surfactants helps to provide insight into the mechanisms ruling the phenomenon.