Hyperspectral (HS) imaging bridges conventional imaging into spectroscopy and generates a spatial map of spectral variations. On the one hand, in HS imaging, the effect of the background on the final spectra has to be removed or managed. On the other hand, there are important classes of materials that need to be immobilized for investigation. In this Letter, we introduce acoustic trapping (AT) for contactless, nondestructive, and easy-to-implement immobilization of particles of up to several mm sizes, subjected to HS imaging experiments. We apply and validate the combined HS-AT apparatus for the identification of plastics, which these days have caused a multifaceted environmental pollution threat. We show that fluorescent HS imaging provides distinguishable fluorescent spectral signatures for an array of different acoustically trapped plastics. Moreover, the HS-AT enables tomographic spatio-spectral information of multi-component plastic samples by means of their acoustically controlled rotation. The integrated HS-AT has the potential to serve as a benchtop identification device.