Valorising household solid waste through the creation of new products based on recycled materials is a necessary task to meet new environmental demands. During the last 30 years, wood-plastic composites (WPC) are been used to obtain materials lighter than wood, with mechanical properties higher than plastic and more resistant to moisture and insects. Thus, the recycling of plastic wastes, especially thermoplastics as polyethylene terephthalate (PET) and sawdust - fine particles of wood from woodworking industries - are suited basic materials for WPC. Indeed, to decrease the cost and time of experimental tests to design a new composite made from recycled PET and Chilean Radiate pine's sawdust, this work proposes to study the effective elastic properties (EEP) using a finite element simulation of a representative volume element (RVE) with periodic boundary conditions in the commercial software Digimat-FE. Density, modulus of elasticity (MOE) and Poisson's coefficients are estimated for composite materials made with 0.05 to 0.35 volume ratio of sawdust. The Voigt and Reuss mean-field homogenisation approaches are also given as upper and lower limits.