What causes the gear not to go into reverse on a 1999 gmc Yukon?

Call your local GM dealer (or go online) and check for recalls or campains on your vehicle cocerning this problem.

If the SHIFTER will not go to the reverse position check for an obstruction in the shifter linkage from where the steering shaft exits the cab down along the firewall to the frame where there is some type of bell crank that changes the back and forth movement of the shifter linkage to rotation force connected to the side of the transmission; if there's no reason for the linkage to be bining your next stop is at a reputable tranny shop. Call the BBB and ask.