A novel finite element model with equivalent meso-mechanics theory is proposed herein to simulate the dynamic structural transitions of the double strand DNA (dsDNA) under external loading. Moreover, the meso-mechanics of dsDNA molecules is then studied based on the proposed model, including the base-stacking interaction between DNA adjacent nucleotide base pairs, the Hydrogen bond of complementary base-pairs and electrostatic interactions along DNA backbones. Experiments on single DNA molecules have shown that the abrupt structural transition between states of different extensions can be driven by stretching/twisting (Figure 1). However, the simplest extensible wormlike chain model is limited to completely represent the mechanical behavior and structural transition of dsDNA under large external force/torque. Accordingly, the dynamic/transient finite element method with material/geometrical nonlinear properties is applied herein to comprehensively understand the mechanical behavior of dsDNA under external loading. In this research, the finite element method based on the continuum mechanics is applied to describe the deformation of dsDNA backbone, and the novel equivalent theory is introduced to simulate the quantum mechanical characteristics of the Hydrogen bond force and stacking interaction between base pairs. Good agreement is achieved between the numerical simulation and single molecular manipulation experimental result. Furthermore, the numerical dsDNA stretching model would be used to study the DNA conformational change driven by the binding of proteins/enzyme to double helix, such as Rec A or Rec BCD protein.