The late Cenozoic extension in the Rio Grande rift of north-central New Mexico was predominantly accommodated by the north-south–trending Pajarito and Sangre de Cristo normal faults and the intervening east-northeast–striking predominantly strike-slip Embudo fault. Using this segment of the rift as our primary example, we have analyzed a series of three-dimensional nonlinear elastic-plastic finite-element models to assess the role of mechanical interactions between pairs of en echelon rift-scale listric normal faults in the evolution of intervening relay zones. The model results demonstrate that under orthogonal extension and an overall plane-strain deformation, relay zones may evolve in a three-dimensional strain field and along non-coaxial strain paths. The extent of non-plane strain and non-coaxial deformation depends on the fault overlap to spacing ratio, the relative orientations of the bounding faults, and the structural position within the relay zone. The model-derived minimum compressive stress vectors within the relay zone are oblique to the regional extension direction throughout the deformation. Within the Rio Grande rift of north-central New Mexico, the occurrence of northerly striking Neogene faults suggestive of east-west extension in the Española and the San Luis Basins, geographic variations in the vertical-axis rotations from paleomagnetic studies, and secondary fault patterns are consistent with the near-surface variations in the strain field predicted by the model. The model suggests that interaction between the Pajarito and the Sangre de Cristo faults may have played a major role in the evolution of this segment of the rift.