Abstract: Traditional numerical methods face the challenges posed by abundant variables and approximation errors, as well as difficulties in ensuring stability. To fulfill these gaps, this article proposes an analytical method for the first time to achieve higher precision, lower complexity, and strong feasibility in integrated energy system analysis. As the first part of the serial studies, this paper focuses on the analysis of the natural gas system(NGS). First, the generalized analytical solution to the gas flow dynamics is derived and the transformation from partial different equations(PDEs) to algebraic equations without approximation errors is realized. Based on the analytical properties, the equivalent representations of the branch and network models in NGS are developed in sequence to further reduce the model complexity. The simulations in different cases indicate the significant superiority of the analytical method in accuracy and efficiency. With a similar computational cost, the analytical method can improve the accuracy dozens of times over the numerical methods.