Mechanical vibrations are a part of several industrial equipment,machinery, systems and vehicles being used in our day to day life. Damping of such unwanted vibrations have been of utmost importance for several industrial operations.Polymer composites have proven to be an effective solution for damping of such vibrations. This study uses finite element methods to analyze the effect of change in key influential parameters on the damping capability of the polymer composite models. The damping capability is measured in terms of 'loss factor' tan $\delta$ which can be expressed as the ratio of of loss to storage modulus of the composite model.Finite element software ABAQUS is used for modelling the polymer composites. This study analyzes the damping properties of two types of polymer composites. The first polymer composite model is made of spherical elastic inclusions dispersed in a cubical viscoelastic matrix. The composite model also consists of a viscoelastic interphase region between the spherical inclusions and the matrix. The finite element model is subjected to mixed boundary conditions and a normal strain is applied on one of the faces. The damping properties are studied over a range of vibration frequency from $10^{-8}$/s to $10^{2}$/s.The study analyzes the effect of interphase region, volume fraction of inclusions and loading frequency on overall damping capability of the composite model.The second part of the study analyzes the damping properties of a model with sinusoidal carbon nanotube as inclusions dispersed in a cuboidal viscoelastic matrix. The finite element model is again subjected to mixed boundary conditions with a normal strain acting on one of the faces with frequency ranging from a $10^{-8}$/s to $10^{2}$/s. The effect of change in input parameters like waviness of nanotube inclusions ,volume fraction and loading frequency is studied. A sensitivity analysis is conducted to understand how the peak damping capability is effected by change in input parameters of composite material properties. Sensitivity analysis is conducted on second model with nanotube inclusions inside a viscoelastic matrix. The elastic modulus of inclusions and matrix is varied within a pre-decided range while keeping the boundary and loading conditions same.