Expanded polystyrene (EPS) is an attractive research area in the field of construction engineering. Its ultra-lightweight properties, high compressibility, and environmental-friendly characteristics make it ideal for the use as a compressible backfilling material for embankments, a filling material behind retaining walls and many other applications. Consequently, the compressive strength is one of the important properties for engineers. To this end, this paper aims to create a simplified elastoplastic model for the uniaxial unconfined compressive behavior of EPS. The developed model can predict the plastic stress–strain behavior of EPS using only its elastic modulus. A mathematical curve fitting model was developed by testing several 50 × 50 × 50 mm cube specimens under the test setup of a 50 kN uniaxial loading machine. Then, the proposed model was validated through the elastoplastic behavior in ABAQUS, by creating a finite element model for the described test setup. It was found that the proposed experimental test setup resulted in reasonable stress–strain behavior for EPS, similar to that indicated in the literature. Also, the presented mathematical model can accurately predict the stress–strain behavior of EPS, which was validated using the elastoplastic response in ABAQUS.