N.M. Admin. Code § 18.31.3.6
The objective of this rule is to prohibit or regulate certain modes of transportation on limited access highways. Interstate highways are designed for motor vehicles. There is an inherent danger anytime motorized and non-motorized modes of transportation mix. There are, however, reasons for allowing bicycles on rural interstates, e.g., facilitating bicycle touring and recreation can benefit a state's economy; most western states, including four of the five states contiguous to New Mexico allow bicycles on the shoulders of interstate highways; interstate shoulders provide a less dangerous route for bike touring than some alternative rural highways; and, some bike touring routes in New Mexico can only be pursued by riding on the shoulders of some rural interstates. This rule is designed to delineate which modes of transportation are prohibited on interstates and to establish the conditions under which bicycles may be operated in interstate highways right-of-way. Allowing bicycles on the shoulders of some interstate highways is not intended to stand as a route recommendation, nor to imply that such shoulders are safer for bicyclists than other routes.
N.M. Admin. Code § 18.31.3.6