Measurements and simulations of the radial distribution of the thermal birefringence components, An and n(00) - n(rn) and the average birefnngence, , in free quenched tubes and rods of polystyrene (PS) and polycarbonate (PC) at different initial temperatures were carried out The thermal stress and birefringence components were simulated using the linear viscoelastic and photoviscoelastic constitutive equations combined with the first-order rate equation for volume relaxation and the master curves for the Young's relaxation modulus and strain-optical coefficient functions of polymers The numerical procedures used to discretize the governing equations using finite difference method were described The obtained numerical results provided the evolution of stress and birefnngence components with time during and after quenching and an explanation of the measured residual birefnngence distribution in quenched tubes and rods It was also found that the thickness of the slices removed from the samples to measure the thermal birefringence components, An and n(00) - n(rn) was critical, in particular, when the initial temperatures were close to the glass transition temperature of polymers With an increase of the initial temperature during quenching, a better agreement between the simulated and measured birefnngence components was obtained POLYM ENG SCI, 51179-200, 2011 (C) 2010 Society of Plastics Engineers