For megavoltage radiotherapy photon beams, EGS4 Monte Carlo calculations show, and experimental measurements confirm with an accuracy of 0.2%, that glass or quartz-walled vials used in Fricke dosimetry increase the dose in the Fricke solution. This is mainly caused by increased electron scattering from the glass which increases the dose to the Fricke solution. The dose perturbation is shown to vary from nothing in a 60Co beam up to 2% in a 24-MV beam. For plastic vials of similar shapes, calculations demonstrate that the effect is in the opposite direction and even at high energies it is much less (0.2% to 0.5%).