When a DNA in its nature double-helical state is stretched by an external force, its length undergoes a sharp extension from the B-form to the 1.7 times elongated S-form. This phenomenon is investigated in the framework of a model of a double-stranded with basepair interactions and bending. Shape equations governing the structure of the DNA under external forces and torques are derived using a classical mechanical approach. The first-order nature of the B- to S-form transition is revealed clearly in terms of an effective potential with a barrier separating these two states. All the structural properties of the DNA in both forms can be calculated in detail. The configurations of the double strands, relative extension, amount of self-untwisting and the threshold stretching force of the DNA under stretched are obtained and compare well with experimental observations.
