A study has been made of a SEIR influenza model with disease resistance in this paper, followed by a calculation of the basic reproduction number of the model by using the method of finding the maximum eigenvalue of the reproduction matrix. It is testified that under the condition of Rc<1, there is only a disease free equilibrium point, with the disease free equilibrium point locally asymptotically stable. When Rc>1, there is a unique endemic equilibrium point in the equation system, with Lyapunov function constructed to confirm the global stability of the endemic equilibrium point. For the first time, the finite element method is used for a numerical simulation, which is consistent with the theoretical analysis. Meanwhile, when compared with the Runge-Kutta method, the proposed process provides a new method for the analysis of infectious diseases.