In this paper, mathematical model of mobile communication systems with traffic congestion and interference was considered in an attempt to study/ determine the quality of service rendered by the mobile networks service provider. The model was mathematically characterized; existence and uniqueness of solution was investigated, interference free steady and persistence steady states equilibria was established. Stability analysis was also carried out. For effective understanding, numerical simulation was carried out with classical fourth order Runge-kutta method using Maple-18 software for different interference rate. Finally, the results were analyzed appropriately and relative conclusions were drawn.