A comparative evaluation of existing rate-type constitutive equations is provided for a viscoelastic fluid undergoing accelerated flow. To this end, accurate point velocity and stress birefringence data previously obtained by laser Doppler anemometry and stress birefringence are utilized. For each constitutive equation, the numerical values of constants which yield the best fit with experimental data are determined via non-linear regression analysis. The best agreement between experimental and calculated normal stress differences is obtained with the White-Metzner equation. The success of this equation is attributed to the deformation rate dependence of its viscosity and time constant.