In this study, the strength properties of recycled plastic materials using polypropylene, polyethylene, and high-density polyethylene were evaluated by measuring their compressive and flexural strengths, which are typically measured in cement-concrete pavements, to assess the feasibility of using recycled plastic materials as construction materials for modular pavements that can easily integrate advanced sensors, such as those for future autonomous driving. Two types of recycled plastic (composite resin and high-density polyethylene (HDPE)) and two types of inorganic materials (fly ash and limestone filler) were selected to evaluate the strengths of recycled plastic materials. Specimens for the compressive and flexural strength tests were prepared with four different recycled plastic contents (100%, 80%, 60%, and 40%). The compressive and flexural strengths of the recycled plastic specimens were measured according to the KSL ISO 679 and KSL 5105 methods, and the strength properties were analyzed based on the type and content of the recycled plastic and type of inorganic material used. Distortion and shrinkage problems were observed during specimen preparation using the 100% recycled plastic material. This indicated that inorganic materials must be incorporated to improve the flexural strength and facilitate specimen preparation. The compressive strength of plastic materials was comparable to the 28-day compressive strength of conventional cement-concrete pavements. The compressive strength of the composite resin was approximately twice that of HDPE. The flexural strengths of both the composite and HDPE were in the range of 15–25 MPa, suggesting their suitability as materials for the construction of modular pavement structures. Based on the limited strength test results, we can conclude that the strength properties of recycled plastic materials are similar to those of conventional cement-concrete paving materials. From the strength perspective, we confirmed that recycled plastic materials can be utilized as construction materials for modular pavements. However, further research should be conducted on factors such as molding methods for modular pavement structures based on different types of recycled plastic materials.