Anaerobic processes for the treatment of plastic materials waste represent versatile and effective approach in environmental protection and solid waste management. In this work, anaerobic biodegradability of model aliphatic polyesters, poly(L-lactic acid) (PLA), and poly(ɛ-caprolactone) (PCL), in the form of powder and melt-pressed films with varying molar mass, was studied. Biogas production was explored in batch laboratory trials at 55 ± 1°C under a nitrogen atmosphere. The inoculum used was thermophilic digested sludge (total solids concentration of 2.9%) from operating digesters at the Central Waste Water Treatment Plant in Prague, Czech Republic. Methanogenic biodegradation of PCLs typically yielded from 54 to 60% of the theoretical biogas yield. The biodegradability of PLAs achieved from 56 to 84% of the theoretical value. High biogas yield (up to 677 mL/g TS) with high methane content (more than 60%), comparable with conventionally processed materials, confirmed the potential of polyester samples for anaerobic treatment in the case of their exploitation in agriculture or as a packaging material in the food industry.