DNA is a biological polymer which basic function in the cell is to encode the genetic material. DNA molecules can be considered to be a mechanical structure on the nano-level. There are different approaches to studding the mechanical properties of the DNA molecule (experimental, theoretical modeling). A number of mechanical models of the DNA double helix have been proposed so far. Different models are focusing on different aspects of the DNA molecule (biological, physical and chemical processes in which DNA is involved). A number of models have been constructed to describe different kinds of movements in a DNA molecule: asymmetric and symmetric motion; movements of long and short segments; twisting and stretching of dsDNA, twist-opening conditions. Some models have, for example, been made for circular double-stranded DNA molecules in viral capsids. We are discussing here polymer models, elastic rod models, network models, torsional springs models, soliton -existence supporting models and multi pendulum/multi chain models, emphasizing specifies of each model. Hedrih (Stevanović) and Hedrih, gave several mechanical models of double DNA. In their models DNA is in a form of homogenous multi-chain/multi-pendulum system which oscillatory signals can be considered trough a system with fixed and with free ends. The models differ in the way of coupling between the material (mass) particles. They’re several types of these models: Model with ideally elastic properties, Model with hereditary properties and Fractional order model.