An integrated energy system with multiple types of energy can support power shortages caused by the uncertainty of renewable energy. With full consideration of gas network constraints, this paper proposes a multi-energy inertia-based power support strategy. The definition and modelling of gas inertia are given first to demonstrate its ability to mitigate power fluctuations. Since partial utilization of gas inertia can influence overall gas network parameters, the gas network is modelled with an analysis of network dynamic changes. A multi-energy inertia-based power support model and strategy are then proposed for fully using gas-thermal inertia resources in integrated energy systems. The influence of gas network constraints on strategy, economy and power outputs is analyzed. Special circumstances where the gas network can be simplified are introduced. This improves the response speed and application value. The feasibility and effectiveness of the proposed strategy are assessed using a real scenario.