Abstract-Ventilation is one of the key safety tasks in underground mines. Determination of the airflow through mine openings and ducts is complex and often requires the application of numerical analysis. The governing equations used in the computation of mine ventilation are discussed in matrix forms. The aim of this paper is to compare the most frequently used numerical analysis methods, which includes Newton-Raphson and the Linear Theory. It is the challenge of this study to investigate the influence of the initial flow rates and the fans in the network. A simulated mine ventilation network is represented in order to examine the two numerical methods. The numerical results acquired from Newton-Raphson method exhibited faster rate of convergence in comparison to those of the Linear Theory method. The mine ventilation networks are less expanded, therefore, the Newton-Raphson method converges faster. On the other hand, when using computational tools and software the advantage of faster convergence becomes less important, and therefore the Linear Theory method will be more preferred.