Production of three-dimensional parts in 3D printing process gains growing importance in various fields, such as: aviation and car industry, architecture, medicine, dentistry, etc. Mechanical performance is an important users’ requirement for manufacturers of 3D printed parts. Furthermore, printed part highly depends on process parameters, position and orientation of the printed part, and performances of the 3D printer which prints the part. In this paper, based on experimental results, an artificial neural network has been used for modeling the dependence of process parameters and object orientation during printing, on the one side, and tensile strength as very important mechanical performance, on the other side. After establishing abovementioned dependence, the developed neural network has been used as a fitness function for the genetic algorithm while the genetic algorithm has been created for the optimization process. The result of optimization process was a set of optimal process parameters and part orientation giving the maximum tensile strength. The results have shown acceptable potential of the developed methodology for optimizing the 3D printing process as a complex engineering problem.