A three-dimensional collapse mechanism that can consider a combined collapse of the tunnel roof and the side walls is proposed in this work. The three-dimensional upper bound support pressure is formulated with the power balance principal in the upper bound theorem. The nonlinear Mohr-Coulomb failure criterion is used to replace the commonly used linear MohrCoulomb failure criterion. The method has been validated by a series of examples, in which the three-dimensional collapse mechanism and support pressures are in a good agreement with the numerical results and solutions found in the literatures. Furthermore, sensitivity analyses of the geotechnical and geometrical parameters on the support pressure are conducted and the collapsing range is measured. The results show that a higher value of nonlinear failure coefficient, tensile strength, initial cohesion and tangential internal friction angle can increase tunnel stability, while tunnel stability is threatened by a higher value of burial depth, unit weight, tunnel width and height. The predicted collapse range increases noticeably with the increase of the nonlinear coefficient. This study is of great significance for predicting the three-dimensional safety support pressure and collapse mechanism of tunnel.