Contemporary technologies are employing composite plate materials developed by using various innovative materials (nanostructures, mica structures, etc.). Application of higher-order modes could allow better detection and characterization of defects characteristic of planar plastic and composite structures, mainly due to shorter wavelength. However, excitation of higher-order modes meets many problems, especially in the case of the air-coupled technique, and is not sufficiently investigated. This is relevant in the cases of paper, high-density polyethylene (HDPE), membranes, GFRP, GLARE, CFRP and other composite structures. The objective of the paper was investigation of the excitation and reception of higher-order guided Lamb wave modes in plastic and composite plates. Therefore, it is appropriate to develop new non-contact ultrasonic measurement methods based on the excitation and reception of guided waves for the study of such objects. The obtained results clearly demonstrate the possibility to excite and receive efficiently different higher-order guided Lamb wave modes with very different phase velocities. The presented comparison of the experimental results with the simulation results showed a good agreement. The combination of air-coupled excitation and non-contact reception enables a non-destructive evaluation and characterization of moving plastic objects and composite structures.