In the present work, relationships between the design parameters and the quality of aluminum sheets formed by the flexible stretch forming process (FSFP) were studied. The punch size, objective curvature radius, and elastic pad thickness were selected as the design parameters. The forming quality was expressed as the shape error, which can be defined by error values at the sampling points. The analytical dataset used to obtain the relationships was collected by means of a series of the finite element (FE) simulations including elastic recovery analysis. The relationships were investigated by regression analysis and a neural network that incorporated a backpropagation training algorithm. The neural network model shows a higher capability of estimating the shape error than the regression model. The effects of primary design parameters selected by the regression analysis were investigated for the shape error. This shows that two types of shape error are affected by different parameters. In order to achieve an acceptable forming quality, the optimum combination of the design parameters must be determined. The predictive model based on the neural network approach provides insights into this procedure.