The exploration of structures made of multiple materials is a growing area of research as additive manufacturing processing technologies such as fused deposition modeling (FDM) 3D printing allows for their fabrication. Such a technology allows for rapid prototyping of structural components with complex geometries or spatially distributed materials with different properties and functionalities. By selecting suitable spatial distribution of materials, the performance of structural components can be manipulated and enhanced as per different engineering application needs. For a low-cost design of structural prototypes using 3D printing processes, viscoelastic polymeric materials are often used, having inherent damping properties. In this research, vibration characteristics of thin plates which are axially graded with multiple polymeric materials are investigated. The goal is to understand the influence of material grading on the frequency and damping characteristics of graded plates. Although in literature, material grading along the thickness in designing composite laminates and their vibration characteristics are available, the performance of plates having axially graded viscoelastic polymers have not been investigated yet. Through systematic modeling and experimental plans, vibration characteristics of axially graded viscoelastic plates are presented here. In particular, the damping performance for different grading schemes is evaluated. It is anticipated that such analysis will allow accurate modeling and testing of design prototypes of structural components for future research, such as design and testing of graded panels for enhanced flutter characteristics.