In the last decade, methods to study single DNA molecules under tensile load have been developed. These experiments measure the force required to stretch and melt the double helix and provide insights into the structural stability of DNA. However, it is not easy to directly relate the shape of the force curve to the structural changes that occur in the double helix under tensile load. Here, state-of-the-art computer simulations of short DNA sequences are preformed to provide an atomistic description of the stretching of the DNA double helix. These calculations show that for extensions larger that approximately 25% the DNA undergoes a structural transformation and a few base pairs are lost from both the terminal and central part of the helix. This locally melted DNA duplex is stable and can be extended up to approximately 50-60% of the equilibrium length at a constant force. It is concluded that melting under tension cannot be modeled as a simple two-state process. Finally, the important role of the cantilever stiffness in determining the shape of the force-extension curve and the most probable rupture force is discussed.