A detailed study on the capacitively coupled radio-frequency (CCRF) argon discharge with metastable atom density and the effect pressure has been undertaken. Specifically, dielectric layers of borosilicate glass and alumina were introduced to the discharge to examine their influence on the discharge characteristics and to study the properties of the plasma. A model for the argon plasma based on the three moments of the Boltzmann equation together with the Poisson equation was used. The properties of the argon plasma presented are based on the averaged cycle, especially the electron temperature, the electric potential, and the metastable atom density. The electron temperature and the metastable atom density decreased in the presence of the dielectric layers, whereas the electric potential had a high value. Sensitivity analysis showed that the surface charge concentrations on the borosilicate glass and alumina dielectrics and the gap voltage increased with the increase of the relative permittivity; the plasma parameters also increased with increasing gap voltage.