An epidemic model with non-monotonic incidence rate under a limited resource for treatment is proposed to understand the effect of the capacity of the treatment. This model is investigated and analyzed by Kar and Batabyal. Also this model is modified by Gajendra et. al. We have reinvestigated the model by considering modified non-monotonic incidence rate under treatment. Let us assume that the treatment rate is proportional to the number of infective when it is below the capacity and is a constant when the number of infective is larger than the capacity. Existence and stability of the disease free and endemic equilibrium are investigated for both the cases. Some numerical simulations and analysis are given to illustrate the analytical results.