Summary form only given. This paper proposes a method for choosing the best transmission system expansion plan considering a probabilistic reliability criterion (RLOLE). The method minimizes the investment budget for constructing new transmission lines subject to probabilistic reliability criteria, which consider the uncertainties of transmission system elements. Two probabilistic reliability criteria are used as constraints. One is a transmission system reliability criterion (RLOLETS) constraint and the other is a bus/nodal reliability criterion (RLOLEBus) constraint. The proposed method models the transmission system expansion problem as an integer programming problem. It solves for the optimal strategy using a probabilistic branch and bound method that utilizes a network flow approach and the maximum flow-minimum cut set theorem. Test results on an existing 21-bus system are included in the paper. They demonstrate the suitability of the proposed method for solving the transmission system expansion planning problem subject to practical future uncertainties