Understanding the mechanical properties that determine the flexibility of DNA is important, as DNA must bend and/or stretch in order to function biologically. Recent single-molecule experiments have shown that above a certain loading rate double-stranded DNA is more stable when stretched from the 3' termini than when stretched from the 5' termini. Unfortunately these experiments cannot provide insight into the structural basis for this behavior. We have used molecular dynamics simulations combined with umbrella sampling to study the stability and structural changes of a 30 bp double-stranded DNA oligomer during stretching from either the 3' termini or the 5' termini. At extensions greater than 1.7x the 3' stretched structure is more stable than the 5' stretched structure due to retention of twice the number (80%) of native hydrogen bonds between base pairs and a higher degree of base stacking. This difference results from greater dissipation of the stretch force via conformational flexibility of the phosphate backbone when pulled from the 3' ends, whereas in the 5' stretch the force is borne more directly by the base pair hydrogen bonds leading to rupture. In addition, stretching from the 5' end produces a greater widening of the major groove that increases solvent exposure and hydrolysis of the base pair hydrogen bonds. These results demonstrate that 3' stretching and 5' stretching in DNA are fundamentally different processes.