Linear conservative birefringence measurements of dilute and semi-dilute solutions of the semi-rigid polymer xanthan gum in a glycerine and water solvent are conducted during flow through a disordered fiber bed. Even though the plug flow through the bed contains no average velocity gradient our results show that the xanthan gum molecules stretch, on average, in the direction of flow. The polymer stretch or birefringence increases with the number of fiber interactions within the bed until a steady-state conformation is attained. The degree of stretch increases monotonically with increasing De(pore) (the ratio of a characteristic polymer relaxation time and the characteristic flow time in a bed pore). The results show a number of qualitative differences when compared to those for the flow of flexible polyisobutylene (PIB) (Evans et al., J. Fluid Mech., 28 (1994) 319) through the same fiber bed. In particular, xanthan gum attains a steady-state conformation after convecting 12 pore-lengths in the bed (compared to approximately 25 for the PIB solution) and this value is independent of De(pore) whereas it increased with increasing De(pore) for the flexible polymer. Additionally the steady-state birefringence of the xanthan gum solutions displays no critical De(pore) at which the birefringence increases dramatically (as does the flexible polymer system) and instead exhibits a slow growth with increasing De(pore). These unique results are interpreted and understood using novel Brownian dynamics simulations of a semi-rigid bead-rod polymer model flowing through a simulated stochastic porous bed flow field created via a spectral expansion. Our results show that the simulations can predict most of the experimental results, at least qualitatively, and in some instances quantitatively, and therefore provide an important tool for understanding these complicated phenomena.