Like other Cenozoic continental rifts, the Rio Grande rift in Colorado and New Mexico exhibits prominent flanking uplifts. Several driving stresses and thermal-mechanical processes have been proposed to explain the origin of rift flank relief, which can be modeled to infer lithospheric structure. Although we have identified multiple uplift styles at the Rio Grande rift, only one range-the Sacramento Mountains-is attributable to flexural upwarping of the lithosphere, the process most suitable for geodynamic modeling and interpretation. We demonstrate that two common assumptions in such modeling potentially introduce serious errors. First, presuming only one mechanism acts to uplift the flanks is inappropriate; various forces influence flank topography at different depths and wavelengths and no single one is dominant. Second, the end-member boundary conditions of complete mechanical continuity or discontinuity (broken plate) at the range-bounding normal fault are, in general, not applicable at rift flanks. We examine alternative analytic plate flexure solutions by comparing them to finite element models of footwall flexure at a normal fault in a two-dimensional elastic plate undergoing extension. These simulations indicate that broken plate fits to rift flanks underestimate the plate thickness unless the uplift is large (at least ~1 km), which promotes decoupling between the hanging wall and footwall. If denudation dominates the flank unloading, as may commonly be the case, the best-fit broken plate thickness error can be even greater. Our flexural analysis of the Sacramento Mountains suggests that the Pecos River Valley originated as a flexural downwarp adjacent to the rift flank. Sensitivity tests of least-squares fits to the Sacramento Mountains imply typical plate thickness errors of <20%, although in extreme cases the combined errors may be ~50%. The average effective elastic lithosphere thickness is ~23 km. We find that elastic--plastic models of rift flank flexure are unable to provide meaningful constraints on the thermal structure of continental lithosphere. ¿ 1999 American Geophysical Union