Expanded polystyrene is widely used as a material for packaging, in modern construction as a heat and sound insulation layer, in thermal insulation systems for buildings, as well as tanks and pipelines. It is additionally used in foundry engineering for the production of models which are gasified during the production of castings from ferrous and non-ferrous alloys under the contact with liquid metal. The use of expanded polystyrene products is associated with waste generation, both in production and in consumption. About 40–50 kg/person of polystyrene waste is generated per year. The peculiarity of polymeric wastes is their resistance to aggressive environments. They do not rot and the destruction processes in natural conditions proceed rather slowly, with the formation of harmful substances that poison the environment. Therefore, the problem of the processing of waste from polymeric materials is of great importance, not only from the standpoint of environmental protection, but also due to the fact that in conditions of a shortage of polymer raw materials, this waste becomes a powerful raw material resource. This article describes the prospects for recycling expanded polystyrene wastes in foundry engineering. In this work, the properties of molding and core sands containing a combined binder, consisting of a solution of expanded polystyrene wastes in turpentine and clay were investigated, and their main characteristics (weight during stretching and crumbling) were determined. Molding and core mixtures, which contain only a binder in the form of a solution of expanded polystyrene in turpentine, have a crude strength of not more than 0.01 MPa. The introduction of a mixture of clay in the amount of 2–3% allows a crude strength of the mixture of up to 0.05 MPa to be obtained. After drying, the investigated mixtures containing a solution of expanded polystyrene wastes and clay have a tensile strength of up to 2.1 MPa. Mixtures into which a solution of polystyrene wastes and clay was introduced have an insignificant gas capacity and satisfactory gas permeability.