The fused deposition modelling (FDM) technique involves the deposition of a fused layer of material according to the geometry designed in the software. Several parameters affect the quality of parts produced by FDM. This paper investigates the effect of FDM printing process parameters on tensile strength, impact strength, and flexural strength. The effects of process parameters such as printing speed, layer thickness, extrusion temperature, and infill percentage are studied. Polyactic acid (PLA) was used as a filament material for printing test specimens. The experimental layout is designed according to response surface methodology (RSM) and responses are collected. Specimens are prepared for testing of these parameters as per ASTM standards. A mathematical model for each of the responses is developed based on the nonlinear regression method. The desirability approach, nonlinear regression, as well as experimental values are in close agreement with each other. The desirability approach predicted the tensile strength, impact strength, and flexural strength with a less percentage error of 3.109, 6.532, and 3.712, respectively. The nonlinear regression approach predicted the tensile strength, impact strength, and flexural strength with a less percentage error of 2.977, 6.532, and 3.474, respectively. The desirability concept and nonlinear regression approach resulted in the best mechanical property of the FDM-printed part.