Abstract: Lamina emergent mechanisms that can realize out-of-plane motion are a kind of compliant mechanisms. They mainly transmit motion, force, and energy through flexible joints; therefore, the design of flexible joints is very important. In the design of flexible joints, the primary requirements are the bending performance and the tensile and compressive properties. However, in general, with the improvement of the bending performance of flexible joints, the tensile and compressive properties deteriorate, and the overall performance of the joints is unable to meet the requirements. To realize joints with better overall performance, tension straps of flexible joints were designed in this study. Based on a flexible joint with high flexibility, a new flexible joint named SS-LEJ was designed. According to the equivalent method, the joint's equivalent spring model was created, and the equations needed to calculate the bending equivalent stiffness of the joints were deduced. In addition, a finite element analysis model was created. The equations were verified by theoretical calculations and ABAQUS simulation analysis. The theoretical calculation and ABAQUS simulation analysis results agree very well. To improve the tensile and compressive properties of SS-LEJ, four kinds of tension straps in different positions and shapes of SST-LEJ were designed. Stress analysis was performed, and the finite element analysis results show that SST3-LEJ and SST4-LEJ are the best two kinds of SST-LEJ. The bending performances and the tensile and compressive properties of SST3-LEJ, SST4-LEJ, SS-LEJ, and inverted bending-orthogonal (IBO) joint were compared. The results show that the bending performances of SST3-LEJ and SST4-LEJ are between those of SS-LEJ and IBO joint, and the tensile and compressive properties of SST3-LEJ and SST4-LEJ are better than those of SS-LEJ and IBO joint. This indicates that the overall performances of SST3-LEJ and SST4-LEJ are better, and the design goal is achieved, which provides an effective method for the design of flexible joints.