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This paper focuses on the development of a surrogate model to predict the macroscopic elastic properties of polymer composites doped with spherical particles. To this aim, a polynomial chaos expansion based Kriging metamodeling technique has been developed. The training experimental design is constructed through a dataset of numerical representative volume elements (RVEs) considering randomly dispersed spherical particles. The RVEs are discretized using finite elements, and the effective elastic properties are obtained by implementing periodic boundary conditions. Parametric analyses are reported to assess the convergence of the scale of the RVE and the mesh density. The accuracy of the proposed metamodelling approach to bypass the computationally expensive numerical homogenization has been evaluated through different metrics. Overall, the presented results evidence the efficiency of the proposed surrogate modelling, enabling the implementation of computationally intensive techniques such as material optimization.