Dynamic mechanical analysis DMA is used for characterization of frequency and temperature dependent elastic modulus of polymer materials. The excitations are applied to the sample with a sinusoidal signal. The system response is measured simultaneously, and serves for the identification of frequency dependent elastic modulus. The test sample is usually loaded in a bending mode with different mounting clamps being available. Usually, the fixation of a sample is not ideal and does not meet the theoretical boundary conditions. That results in fixation-dependent natural oscillations of the sample. Thus, a new way of dynamic mechanical analysis for identification of elastic modulus will be presented. The new method enables a non-contact application of force on the sample and a non-contact acquisition of its response. During the measurements, the free-free boundary condition is proposed, as it can be effectively replicated in the experiment. The goal of the newly developed non-contact DMA method is the identification of elastic modulus of the material. The procedure of identification is based on the experimental determination of natural frequencies in conjunction with a method of modal updating of an equivalent numerical model. With the developed method elastic modulus of 17 tested samples was determined. The closeness of the agreement between the results, obtained by measurements, and the results from accessible literature, are displayed.