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A dragonfly can hover, flap its wings for flight and fly vertically for a short distance. The membranous wings of a dragonfly have a high load-bearing capacity for static and dynamic load during flight. The mass of the wings of a dragonfly is only 1%-2% of its whole body but the wings can stabilize its body. The statics properties of biomimetic models were researched. The finite element software ANSYS was used to simulate the dragonfly wing. The veins were simulated by pipe20 with two nodes and the membranes by shell43 with four nodes. The influence of geometrical nonlinearity was taken into account but material nonlinearity. The models were assumed in the elastic range. The three-dimensional model of the dragonfly wing was reconstructed using reverse engineering software Imageware. The veins of dragonfly wing were drawn with AutoCAD and the membranes were added with ANSYS. The finite element models imitating the dragonfly wing were established by using free meshing. The finite element models of the dragonfly wing were simulated with structural statics. The deformation, the stress and the strain of the models under loads were analyzed respectively. The loads include the uniform load, the bending moment and the torque. Under the uniform load, the deformation of the finite element model imitating a dragonfly wing is very small, and increases gradually from the base to the wing tip. The base of the model bears heavy stress, the middle parts smaller, and the wing tip the least. The strain shows a radial pattern along the longitudinal veins, and reduces gradually from the base to the wing tip of the model. Under the bending moment, the deformation and the rotation angle around y axis increase gradually from the base to the wing tip of the model. The heavy stress and strain are mainly concentrated on the base of the model. The small stress and strain are acted on the middle parts and the wing tip. The distribution trend of the stress and strain is in substantial agreement. Under the torque, the finite element model imitating a dragonfly wing deforms only a little as a whole. The heavy deformation is mainly concentrated on the leading edges and the rear edges of the model. The smaller deformation is acted on the middle parts and the least deformation on the base. The maximum stress and strain occur at the middle parts of the model. The minimum stress and strain occur at the base of the model. The dragonfly wing is a two-dimensional truss structure with excellent rigidity. The dragonfly wing deforms only a little under loads. It is shown that the grid structures of the dragonfly wing deforming together at the boundaries of veins and membranes have excellent integrity. The understanding of dragonfly wings' characteristics provides some reference for improving the properties of two-dimensional composite materials through biomimetic designs. [ABSTRACT FROM AUTHOR]