In gas turbine engines, the secondary air system (SAS) plays a vital role by supplying air for turbine blade cooling, preventing hot gas ingestion into disk cavities, and sealing bearing chambers. To accomplish these tasks, SAS mass flow rates must be calculated with high accuracy. Because of the complex geometries of the SAS flow path and the challenges of preparing a CFD model, one-dimensional (1D) flow modeling is widely used as an industry standard for internal airflow calculations. The flow domain is represented with 1D flow elements such as K-losses, Cd-losses, orifices, and pipes. This paper presents the theory behind an in-house computer program developed for steady-state 1D flow network calculations with both compressible and incompressible fluids. The program iteratively solves the conservation of mass, momentum, and energy equations using the appropriate loss correlations for each flow element. In this formulation, both total and static pressures are solved simultaneously at network nodes, followed by a thermal calculation cycle. Mass flow rates are modeled as functions of inlet total pressure and exit static pressure. The Newton–Raphson method was chosen to solve the nonlinear system of equations because of its convergence speed and numerical stability.