The mass application of FDM technology is slowed down due to the difficulty of selecting 3D printing parameters in order to manufacture an article with the required characteristics. This paper reports a study into the impact of 3D printing parameters (temperature, print speed, layer height) on mechanical parameters (strength, elasticity module), as well as on the accuracy of printing and roughness of the surface of a specimen based on thermoplastic (PLA plastic). Several batches of specimens were fabricated for this study in accordance with ASTM D638 and ASTM D695, which were tested for tension, geometric accuracy, and roughness. Based on the experimental data, regression analysis was carried out and the functional dependences of the strength, elasticity module, printing precision, roughness of a surface on 3D printing parameters (temperature, speed, thickness of the layer) were constructed. In addition, the derived mathematical model underlying a method of non-linear programming has established such printing parameters that could provide for the required properties of a structure. The analytical dependences reported in the current work demonstrate a high enough determination factor in the examined range of parameters. Using functional dependences during the design phase makes it possible to assess the feasibility of its manufacture with the required properties, reduce the time to work out the process of printing it, and give recommendations on the technological parameters of 3D printing. The recommendations from this study could be used to make PLA-plastic articles for various purposes with the required properties