Optimizing the processing parameters of fused deposition modeling is a challenging task due to the significant number of factors that influence the quality of the fabricated parts. Therefore, optimizing the dimensional accuracy, surface roughness, or mechanical properties usually requires a considerable amount of test samples. In the presented work, the design of experiments approach was used to minimize the number of tests needed to optimize the factors. Most of the work available in literature did not investigate the interactions between the factors or their second-order effects on the strength and stiffness of fused deposition modeling parts. In this work, the effects of the layer thickness, extrusion temperature, and infill percentage are investigated and optimized to achieve the optimum strength and stiffness of the fabricated parts. The response surface method was used to investigate the interaction effects and second-order effects on the tensile strength and elastic modulus of the fabricated samples. It was found that some interaction and second-order effects exist and affect the strength and stiffness of FDM parts. Generally, increasing the extrusion temperature and infill percentage increase the tensile strength and the elastic modulus. In addition, the predicted data matches the experimental results well. However, multi-objective optimization is needed when choosing the layer thickness.