how do you model a transmission line at dc?
A transmission line at DC is modelled as two resistances, each calculated from the length, gauge and resistivity of its conductors.
Often it is specified as R per length, e.g. 10 Ohm per 1000 feet. With coax, the core (or center) will have a different R-per-distance than the shell, due to the difference in cross sectional conductive area of each.
Here's an example for coax:

From http://www.dbsinstall.com/diy/CoaxCableTypes.asp
As an aside, transmission lines  are often also used to supply power in tandem with communication signals.
DC is then the mode of choice over AC for power supply, since the lines distributed L and C will have no effect on impedance matching or power losses, and only the R matters. It can be measured with an Ohm meter.
That same R forms the basis for the line's attenuation, although with increasing frequency the R increases because the currents flow in a smaller (outer shell) cross section of the conductor due to &quot;skin effect&quot; which worsens as f increases.
Moreover, the signal is AC coupled, and the power is DC coupled with a throttle for higher frequencies.