The flight performance of insects is strongly affected by the deformation of the wing during a stroke cycle. Many insects therefore use both active and passive mechanisms to control the deformation of their wings in flight. Several studies have focused on the wing kinematics, and plenty is known about the mechanism of their passive deformability. However, given the small size of the vein-joints, accurate direct mechanical experiments are almost impossible to perform. We therefore developed numerical models to perform a comparative and comprehensive investigation of the mechanical behaviour of the vein-joints under external loading conditions. The results illustrate the effect of the geometry and the presence of the rubberlike protein resilin on the flexibility of the joints. Our simulations further show the contribution of the spikes to the anisotropic flexural stiffness in the dorsal and ventral directions. In addition, our results show that the cross veins, only in one joint type, help to transfer the stress to the thicker longitudinal veins. The deformation pattern and the stress distribution in each vein-joint are discussed in detail. This study provides a strong background for further realistic modelling of the dragonfly wing deformation.