© 1969-2012 IEEE. Natural gas is an important fuel source in the power industry. Electricity and natural gas are both energy that can be directly consumed. To improve the overall efficiency of the energy infrastructure, it is imperative that the expansion of gas power plants, electricity transmission lines and gas pipelines can be co-planned. The co-planning process is modeled as a mixed integer nonlinear programming problem to handle conflicting objectives simultaneously. We propose a novel model to identify the optimal co-expansion plan in terms of social welfare. To evaluate the robustness of plans under different scenarios, the flexibility criterion is used to identify each plan's adaptation cost to uncertainties, such as demand growth, fuel cost and financial constraints, etc. We developed a systematic and comprehensive planning model to understand, develop and optimize energy grids in order to reach higher social welfare, and is therefore of great importance in terms of supporting and guiding investment decisions for the power and gas industry. Meanwhile, we use the sequential importance sampling (SIS) to perform scenario reduction for achieving a higher computational efficiency. A comprehensive case study on the integrated IEEE 14-bus and a test gas system is conducted to validate our approach.