A new methodology has been developed to model the viscoelastic behavior of solids using a general spectrum function. Not all materials can be modeled using simple Kelvin-Voigt (K-V) or Maxwell elements where the viscoelastic parameters are constants. There is a need for a general spectrum function that can be used to model the Lame' functions which constitute all properties of interest. Thus far, there is no method like the one presented in this study that can determine the moduli of viscoelastic materials. This study develops a methodology by which the time dependent properties of homogeneous and non-homogeneous materials may be modeled. Once the Lame' functions are determined, the Principle of Correspondence is applied to the elastic equations to determine the necessary properties. In uniaxial tension the time dependent strain, modulus, Poisson's ratio, and compliance are determined. The time dependent deflection is determined for beams in flexure. Where applicable, parameters determined from the analytical model are compared to the available experimental data. Good agreements are found between the analytical and experimental data sets.