Rail transport is widely regarded as an efficient and environmentally sustainable mode of mobility, although lifecycle emissions from infrastructure can diminish its ecological benefits. This study assesses a novel slab track system design that replaces conventional concrete components with recycled polymeric composite sleepers, supporting circular economy objectives. Analytical calculations (per EN 16432-2 and EN 13230-6) and finite element analysis (FEA) were conducted on a 2.6 m polymeric composite sleeper model under static vertical loading. The results demonstrate that bonded base layers comprising asphalt and hydraulically bound materials reduce bending stresses within the sleeper to 1.307 N/mm2, substantially below the 5.50 N/mm2 observed without bound layers and well below both characteristic fatigue limits. Laboratory validation via strain-gauge measurements corroborates the numerical model. Despite minor torsional effects from first-batch production, the polymeric composite sleeper design is structurally viable for slab track applications. The methodology is directly transferable to alternative composite designs, allowing material-based adaptation of mechanical performance. These findings support the use of recycled polymeric composite sleepers in slab track systems, combining structural adequacy with enhanced circularity. Further research can base itself on the findings and should incorporate long-term durability testing.