This paper proposes three methods for choosing the transmission system expansion plan considering three reliability constraints, which are deterministic reliability criterion, probabilistic reliability criterion and security criterion based on N-α contingency in order to give more successful market operation. The proposed method minimizes total investment cost It models the transmission system expansion problem as an integer programming one. The method solves for the optimal strategy using a branch and bound method that utilizes a network flow approach and the maximum flow-minimum cut set theorem. The 21 bus system case study results demonstrate that the proposed method is practical for solving the power system expansion planning problem subject to practical future uncertainties.