The 1991 global merged interaction region (GMIR) shock is a strong forward shock observed from Voyager 2 on day 146 of 1991 at 34.6 AU at the leading edge of the 1991 GMIR. This shock is the strongest shock ever identified from the Voyager data in the distant heliosphere. In this paper we study the evolution and propagation of the 1991 GMIR shock outside 34.6 AU in the upwind direction taking into account the influence of interstellar pickup protons. We calculate the time, location, and various variables of this shock in the subsequent 400 days. We use the shock interaction model to develop a R,t-simulation code to study this problem. The model treats the shock as a surface of discontinuity with zero thickness and uses the method of characteristics to study the evolution of the solar wind in the disturbed region. This model can accurately calculate the propagation speed and the strength of the shock. The numerical solution shows that as the GMIR shock propagates from 35 AU to 150 AU, the shock speed decreases monotonically from 543 km/s to 478 km/s and the density ratio decreases from 2.55 to 2.09. The solar wind proton temperature and the pickup proton temperature on two sides of the shock decrease monotonically with increasing heliocentric distance. Across the shock the solar wind proton temperature ratio is high, namely, ~22 at 35 AU and ~11.5 at 150 AU, while the pickup proton temperature ratio is an order of magnitude smaller: ~2.1 at 35 AU and ~1.8 at 150 AU. ¿ 1999 American Geophysical Union