Tube Hydroforming Process (THF) is heavily affected by the pressure-displacement diagram, and adjustment of the raw tube. Three common defects of the process are bursting, buckling and wrinkling. In this work, the leading conditions to wrinkling defect have been studied. Proper criteria are required to predict wrinkling condition, and to quantify wrinkling when subjected to various pressure-displacement diagrams. A variety of criteria have been presented by researchers, most of which are suitable to a specific geometry. In current work, two criteria are considered namely, the strain difference and the radius velocity. At first an accurate FEM (Finite Element Model) model of the process have been established and validated. Then based on a number of experiments with different diagram, the process have been simulated and analyzed. According to experiments imbalances between pressure and displacement, improper sitting of tube in the die, poor vacation of the tube and the existence of external tiny particle inside the die, are the reason of wrinkling criterion in the tube. The Response Surface Method (RSM) has been used to model the responses from the finite element analysis. The behavior of the process has been predicted using this model.