This study determined the elastic properties of composites and concretes reinforced with oil shale ash (OSA) particles, a byproduct of oil shale combustion in an electric power plant in Estonia (Auvere). Since 2018, OSA has no longer been classified as hazardous waste in the EU, enabling its reuse in sustainable materials. The present research examined the effect of OSA on the elastic properties of epoxy–OSA and concrete–OSA composites. The experimental results show that the elastic modulus of epoxy resin increases with an increase in the ash concentration, while it decreases in concrete with a higher OSA content. Theoretical models, including the rule of mixtures, finite element method (FEM), Mori–Tanaka method, and Halpin–Tsai method, were used to predict these properties numerically. The rule of mixtures and FEM generally overestimated the modulus for epoxy–OSA, whereas the Mori–Tanaka and Halpin–Tsai methods provided closer predictions. For concrete–OSA, the compressive strength tests followed the LVS EN 12390-3:2019 standards, with elastic modulus conversions being made via IS 456:2000 Clause 6.2.3.1, which showed a variable decrease across different strength classes. The findings highlight the potential of OSA as a reinforcing filler in construction materials, promoting environmental sustainability by repurposing industrial waste while offering mechanical benefits.