The dumbbell model with internal viscosity for a dilute polymer solution is investigated based on a balance of viscous drag and restoring Brownian forces. An approximate method is used to obtain the solution of extensional stress in closed form in the case of steady flow. For different internal viscosities, this parametric study shows different asymptotic regimes of the extensional viscosity as a function of strain rate. This analysis may explain the attenuation of pressure drop in strong flows from a phenomenological point of view.