The stiffness modeling of a family of six degrees of freedom (DoF) parallel mechanisms with configurations of 3-RUPU is presented. The mobility of the mechanisms is firstly analyzed, and then the stiffness analysis and modeling of the family of mechanisms is developed by a novel screw-theory based method. The method employs screw theory as a tool for force analysis and deformation analysis. Based on the developed stiffness model, two global flexibility indices, which refer to the maximum and minimum singular values of compliance matrix, are introduced to evaluate the compliance of parallel mechanisms. Finally, a case study is presented to demonstrate the effectiveness of the method in analyzing and evaluating the stiffness behavior of the presented parallel mechanisms.