Controlled trapping and stretching of DNA molecules is critical for single molecule genomic and polymer physics studies. We present a microfabricated T-junction which can trap and stretch single free DNA molecules using electrophoretic forces (Tang and Doyle, Appl. Phys. Lett. 2007). The device does not require special end-functionalization of the DNA. The purely elongational nature of the electric field allows us to use thin fluidic channels. We show that two physical mechanisms of stretching can occur depending on the length of the DNA relative to the channel width in the junction region. In one case the governing dimensionless group is a Deborah number and in the other a Peclet number. Stable trapping and stretching of DNA molecules up to lengths of 485 kilobasepairs is demonstrated. Applications in single molecule mapping will also be demonstrated.