Abstract: Collapse is one of engineering geological hazard that often occurs at mountain tunnel exit. The prediction of spatial position and occurrence time of the collapse is one of technical problems of the tunneling engineering. The instability criterion and critical distance in loose wall rock at tunnel exit when the collapse occurs are deduced based on the stress-transferring theory. These formulas can be used to forecast the possibility and spatial position of the collapse. At the same time, based on the measured data of vault crown settlement, a grey-synergetic prediction model is established by use of the grey theory and the synergetic theory. Then the instability criterion and the grey-synergetic prediction model are verified by the collapse which occurs in Maanshan tunnel of Zhuji-Yongjia highway. The results show that the spatial position and the occurrence time of the collapse predicted are consistent with the practical situations. It is feasible to use the deduced instability criterion and grey-synergetic theory to predict the spatial position and occurrence time of tunnel collapse. This prediction method has high accuracy and reliability, and it can provide references for the prediction of other collapses at tunnel exit.