Closed-form expressions to describe artificial dielectric layers with finite conductivity are presented. The propagation of a generic plane wave within the artificial material is described by means of transmission line models, where each layer is represented as an equivalent shunt impedance. The given analytical formulas for the shunt impedance are derived assuming finite conductivity of the metal, and thus, also an accurate estimation of the losses within the artificial dielectric is obtained from the equivalent circuit. The expressions account for the reactive coupling between the layers due to higher order Floquet modes, thus remain valid even for extremely small electrical distance between layers.