The ground reaction curve (GRC) is a vital component of the convergence-confinement method, which possesses many applications in the underground space designs. It defines a relation between the tunnel wall deformations and the ground pressure acting on the tunnel walls. Generally, GRC includes descending and ascending branches. According to many researchers, the descending branch trend for the ground pressure stops after the critical deformation, and thus the ground pressure on the support system increases due to the formation of a loosening zone and an ascending branch, and finally, the creation of an ultimate pressure on the support system. In this work, two relations are proposed to determine the ultimate ground pressure acting on a circular tunnel in a continuous medium. It is assumed that the rock mass obeys the elastic perfectly plastic model with a cohesionless behavior in the broken zone. This is accomplished by incorporating the Duncan-Fama solution and the two models of Yanssen-Kötter and Caquot rigid plastic. The ground pressure obtained by the Caquot model shows a better correlation with the Goel-Jethwa equation compared with the Yanssen-Kötter solution.