We have developed a theory for the extension and force of B-DNA tethered at a fixed point in a uniform hydrodynamic flow or in a uniform applied electric field. The chain tethered in an electric field is considered to be subject to free electrophoresis compensated by free sedimentation in the opposite direction. This allows the use of results of free electrophoresis for including the effects of small ions. The force on the chain is derived for a sequence of ellipsoidal segments, each twice the persistence length of the wormlike chain. Hydrodynamic interaction between these segments is based on the long-range limit of flow around the prolate ellipsoids, as derived from equivalent Stokes spheres. The chain extension is derived by applying the entropic elasticity relation of Marko and Siggia (1995 Macromolecules. 28:8759-8770) to each segment for polymer chains under constant tension. We justify this procedure by comparing with extension results based on the Boltzmann averaged orientation of straight, freely jointed segments. Predicted results agree well with recent extension-flow experiments by Perkins et al., 1995. Science. 258:83-87, and with electrophoretic stretch experiments by Smith and Bendich (1990 Biopolymers. 29:1167-1173) on fluorescently stained B-DNA. We find that the equivalence of hydrodynamic and electrophoretic stretch, proposed by Long et al. (1996 Phys. Rev. Lett. 76:3858-3861; 1996 Biopolymers 39:755-759), is valid only for very small chain deformations, but not in general.