Abstract: Based on the continued fraction formulation of the scaled boundary finite element method (SBFEM), a continued fraction formulation for infinite acoustic fluid of uniform cross section was proposed and high-frequency and doubly asymptotic continued fraction formulations were derived. Computational efficiency was compared between the proposed continued fraction formulation and the dynamic mass matrix, which were both used to model an infinite acoustic fluid of uniform cross section. It was found that the computational efficiency of the former was higher than that of the latter. The transient response of an infinite acoustic fluid of uniform cross section under upstream excitation was analyzed using the proposed formulation. Numerical results showed that the stability and convergence of the high-frequency continued fraction formulation need further improvement, while the stability and convergence characteristics of the doubly asymptotic continued fraction formulation are both better, meaning that it can accurately model an infinite acoustic fluid with uniform cross section.