The estimation of equivalent optical parameters of the nanostructure absorber materials will help to understand its absorption, reflection and radiation characteristics. The effective optical parameters of the metamaterials are estimated by the S-parameters proposed by Smith in 2002, which assumes the nanostructure metamaterials to be homogeneous bulk material, without reflecting the relationship between the equivalent optical parament, the geometrical structure and material characteristics. Here an analytical theory in which the Drude-Lorentz model is adopted to describe the dispersion relations of metamaterials′ absorptive characteristics in infrared (IR) is presented. Based on the effective electron density and the equivalent circuit analysis, a functional description between the geometrical parameters and its Drude-Lorentz model parameters has been built. This analysis on periodic arrangements of rectangular structures array is performed. The model establishes the quantitative relationship between structure parameters, material parameters and its optical constants. It offers an accurate prediction for their dispersive behavior at near-IR wavelengths.