Plastic identification is a fundamental step in material and chemical recycling. Overlap between plastics is a common limitation of existing identification methods, and it is necessary for plastic waste to be shredded and spread over an area to avoid overlapping between flakes. However, this process decreases sorting efficiency and also increases the risk of misidentification. This study specifically focuses on plastic sheets and aims to develop an efficient identification method for overlapping plastic sheets, by using short-wavelength infrared hyperspectral imaging. The method is based on the Lambert-Beer law and is simple to implement. We consider a practical situation with a reflection-based measurement system and demonstrate the identification performance of the proposed method. The tolerance of the proposed method against error sources of measurement is also discussed.