An adaptive, heuristic, nonlinear mathematical model (AHNM) was proposed to optimize the loading path of successful tube hydroforming process through adaptive minimization of the internal pressure and axial load by using Multiple Ridge Regression (Machine learning technique). The AHNM model was implemented, solved, and optimized, and it was found that increasing the number of steps and starting with small increment enables the mathematical model to capture the non-linearity of the real model, which leads to minimizing the system requirements. In this paper Finite Element Modelling (FEM) was developed to verify and test the validity and reality of the implemented loading oaths from the AHNM model for hydroforming of T-shape tube having an elliptical protrusion. The objective function was measured, and the results of minimum thickness, and maximum protrusion height were verified. Besides, the tube was formed with a well wall thickness distribution. Consequently, it is confirmed that developing an adaptive heuristic nonlinear mathematical modelling is effective for obtaining a Loading Path for Hydroforming of a Tube Having an Elliptical Protrusion.