In ultimate asseismic design of ductile frame structures, plastic deformation and plastic hinge are generally permitted, and some preferred failure modes are often selected. It is an important problem that whether the designed structure collapses according to the designed failure mode, because of the large uncertainties included in external loads and member strength. In this paper, an identification procedure of failure modes for frame structures is developed, and the likely collapse modes of frame structures under uncertain load and member strength are investigated under assumption of normal distributed and non-normal distributed external loads and member strength. It is found that the occurrence order of likely collapse mode is much influenced by the distribution of the random variables. The occurrence order of collapse modes for column over designed structures are investigated and it is found that the increase of column over-design factor can effectively avoid the story collapse mode in probabilistic means.