Elongation studies are very important for validating the constitutive equations that describe the rheological behavior of fluids. The relaxation of a stretched polymer chain in the flow field has not been investigated in detail thus far. We extended the constitutive equations for predicting the start-up behavior and the power law relationship between the steady-state elongational viscosities and the strain rate. We also determined the steady-state elongational viscosity by fitting the calculated results with the measured values. The calculated results show the power law relationship between the steady-state elongational viscosities and the strain rate. Furthermore, we used these constitutive equations to predict the overshoot of the viscosities and stresses at initial stages of the steady elongational or shear flows by considering only one parameter, the stretch relaxation time.