The pressure rate is a key parameter during sheet hydroforming. To investigate the influence of pressure rate (the increment of pressure per unit time) on the thickness of aluminum alloy cylinder-shaped part flange under the action of thickness normal stress, a finite element model of hydroforming was established. Variations in thickness of the flange of cylinder-shaped parts were simulated at different pressure rates under the same forming parameters, such as friction coefficient, forming pressure, and loading path. For the convenience of the study, the thickness variation range was divided into three intervals, namely, the fast growth area, the slow growth area, and the fluctuation area, when the pressure rate is larger than 1.25 MPa/s. The variation of the thickness of the flange in these three intervals was analyzed and the relation between the pressure rate and the maximum flange thickening rate was obtained for the different intervals. The influence of the pressure rate on the thickness of cylinder-shaped part flange was obtained. Using a quadratic polynomial curve fitting method, a prediction equation for the maximum rate of thickening of cylinder-shaped part flange was established, by which maximum flange thickness can be predicted for different pressure rates. Experimental verification was also carried out. It was found that the experimental results are in good agreement with the simulation results. The prediction equation can provide useful reference and experimental basis for the selection of hydroforming deep drawing process parameters of aluminum alloy cylinder-shaped parts and the trial production of typical parts. [ABSTRACT FROM AUTHOR]