The long-range hydrodynamic interaction between DNA and agarose gel is treated by modeling the gel as a uniformly porous medium, characterized by Debye's hydrodynamic shielding length L. We derive the liquid now field around a solid sphere moving through the gel and the hydrodynamic friction of the sphere. These results are used in the hydrodynamic interaction between DNA and the gel during electrophoretic stretch and relaxation of stretched DNA. Experiments by Gurrieri, Smith, and Bustamante (Proc. Natl. Acad. Sci. USA 1999, 96, 453) lead to an estimate oft = 4 x 10(-8) m for the shielding length of 1.2% agarose gel. The critical trapping force in such a gel is found to be 29 pN, consistent with results reported by Gurrieri et al. (1999). If the unwinding of the double helix at the gel contact is essential for trapping, addition of salt should cause a significant increase in the critical field strength for trapping DNA. Relaxation of the length and of the tether force of initially stretched DNA is described by a balance between the elastic forces (tension gradients) of DNA and hydrodynamic friction. Brownian motion is introduced in an approximate way. Its effect on the relaxation is moderate. The influence on relaxation of several factors, including gel porosity and DNA size, is studied. The scaling with DNA size is better for relaxation of the tether force than of the DNA extension, The relaxation of DNA predicted in pure solvent agrees fairly well with experiments by Perkins, Quake, Smith, and Chu (Science 1994, 264, 822).