Preliminary combustor design usually requires that an extensive number of geometrical and operational conditions be evaluated and compared. During this phase important parameters the designer sought after are typically the mass flow rate distribution through air admission holes, associated pressure losses as well as liner wall temperatures. The process is therefore iterative in nature and can become expensive in terms of engineering analysis cost considering the time required to build and execute 3D CFD models. Network codes have the potential to fill the gap during this stage of the design since they can be setup and solved in timeframes that are orders of magnitude less than comprehensive CFD models, essentially leading to cost savings since overall less time is spent on 3D simulations and rig tests. An additional advantage using this approach is that results from the network solution can be applied as boundary conditions to subsequent more detailed 3D models. In this study a commercial flow network tool, Flownex®, was used to model a complete combustor including flow distribution, combustion and heat transfer. The integrated mass, momentum and energy balance is solved using the continuity, momentum and energy equations applied to nodes and elements. These nodes and elements are the modular building blocks, typically semi-empirical and allow users to either select appropriate built-in correlations, or to define using specific equations through scripting. Flow equations are fully compressible and applied to the gas mixture. The chemical composition of the reactants forming during combustion as well as the adiabatic flame temperature is determined from the NASA CEA package incorporated into the solution. Heat transfer mechanisms included in the model are gas-surface radiation, film convection, forced convection in ducts, surface-surface radiation, and 2D axially-symmetric conduction through solid walls. Results produced from the network were compared with test data obtained from the NASA E3 development combustor. Overall good agreement resulted, showcasing the success of the approach followed.