Viscoelastic adhesives, polymers and foams are seen as an area of high growth in the world, due to their intrinsic benefits and critical role in different lightweight structures with passive damping control and glued assemblies widely used in many industrial sectors such as aerospace, land transport, marine and construction. Unfortunately the technical data of such materials provided by manufacturers do not contain all necessary information to predict the behaviour of advanced composite structures using different analysis tools. For this reason, a new inverse technique based on simple vibration tests has been developed to characterise the nonlinear mechanical properties of various viscoelastic materials. This novel approach allows to preserve the frequency and temperature dependencies of the storage and loss moduli of viscoelastic materials in a wide range of frequencies and to analyse structures using high damping tests. The computational effort has been substantially reduced by using an optimisation based on the planning of the experiments and the response surface technique in order to minimize the error functional. This new inverse technique has been tested and successfully applied to characterize the viscoelastic material properties of a 3M damping polymer (ISD-112) used as a core material in sandwich panels under different temperatures.