A process of critical transmission lines identification in presented here. The criticality is based on network flow, which is essential for power grid connectivity monitoring as well as vulnerability assessment. The proposed method can be utilized as a supplement of traditional situational awareness tool in the energy management system of the power grid control center. At first, a flow network is obtained from topological as well as functional features of the power grid. Then from the duality property of a linear programming problem, the maximum flow problem is converted to a minimum cut problem. Critical transmission lines are identified as a solution of the dual problem. An overall set of transmission lines are identified from the solution of the network flow problem. Simulation of standard IEEE test cases validates the application of the method in finding critical transmission lines of the power grid.