Poly methyl methacrylate (PMMA) was melt compounded with different nanoparticles using a twin-screw extruder. Nano TiO2, SiO2 and Al2O3 in 0.5, 1 and 2 wt% were added to the polymeric matrix as reinforcements. Nine polymeric nanocomposite samples were injection molded. Impact strength, Young's modulus, Rockwell hardness-R and cost of raw materials were considered as different criteria. Two procedures of multi-criteria decision making (MCDM) methods were performed for solving material selection problem. Criteria weighting was performed using analytical hierarchy process (AHP). According to weights that obtained from AHP, the alternative ranking was implemented using TOPSIS (the technique for order preference by similarity to ideal solution) and MOORA (multi-objective optimization on the basis of ratio analysis) methods. The results indicated that the addition of nanoparticles to the polymeric matrix was significantly improved mechanical properties. The results showed a 94% and 229% improvement in impact strength for PMMA containing 1 and 2 wt% TiO2 compared to pure PMMA. The results also revealed that hardness and Young's modulus of PMMA were increased by addition of different nanoparticles. The implementation of MCDM methods illustrated that PMMA-2 wt% TiO2 is the best alternative. Also, PMMA-1 wt% TiO2 and PMMA-2 wt% SiO2 are the next alternatives, respectively.