A combination of laser-induced breakdown spectroscopy (LIBS) and artificial neural networks (ANNs) has been used for the identification of polymer materials, including polypropylene (PP), polyvinyl chloride (PVC), polytetrafluoroethylene (PTFE), polyoxymethylene (POM), polyethylene (PE), polyamide or nylon (PA), polycarbonate (PC) and poly(methyl methacrylate) (PMMA). After optimization of the experimental setup and the spectrum acquisition protocol, successful identification rates between 81 and 100% were achieved using spectral features gathered from single spectra without averaging (1 second acquisition time) over a wide spectral range (240-820 nm). Furthermore, ten different materials based on PVC were tested using the identification procedure. Correct identifications were obtained as well. Sorting of the materials into sub-categories of PVC materials according to their charges (concentration in trace elements such as Ca) was performed. The demonstrated capacities fit, in practice, the needs of plastic-waste sorting and of producing high-grade recycled plastic materials.