The energy flow analysis method with both high precision and high computational efficiency is a basic tool to simulate the operation and analyze the interaction between the thermal and electric coupling systems. The traditional iterative numerical method is slow in computation，poor in computability for large-scale problems，and can only obtain the value of the state variable in discrete time series. Moreover，the traditional numerical method to solve electric power flow is not compatible with that to solve the dynamic flow of the heat network，so the alternating iterative solution is often adopted in the dynamic energy flow analysis，which makes the error spread in the iterative process. To solve the above problems，a dynamic energy flow analysis method was proposed based on holomorphic embedding for integrated electricity and heating systems. Through recursive calculation，the continuous analytic function of system state variable with respect to time was obtained. In the calculation process，the solution of electric power system and heating system was obtained jointly. The simulation results show that the maximum error between the algorithm and the Matlab solver is less than 3%，and the calculation speed is increased by more than 30%. Moreover，the algorithm can calculate the system state at any time in the dynamic process according to the holomorphic function.