In this paper, a generalized phasor method (GPM) for modeling gas flow dynamics is proposed and applied in integrated electricity-gas dispatch (IEGD). An accurate dynamic model of natural gas systems is described by partial differential equations (PDEs). In existing studies, PDEs are often approximated by using the finite difference method (FDM), but many variables and constraints are required in that approach. The proposed GPM transforms PDEs into ordinary differential equations (ODEs) by using the Fourier method and then eliminates spatial variables by analytically solving the transformed ODEs. Since spatial differences are avoided, the GPM has fewer constraints and variables than the traditional FDM. Moreover, the GPM contains only linear complex algebraic equations, so IEGD problems based on the GPM can be efficiently solved. In case studies, IEGD models based on the GPM and FDM are compared for two integrated electricity-gas systems. The results illustrate that the proposed GPM and FDM yield similar accuracies, but the GPM has a shorter calculation time than the FDM.