The external bremsstrahlung (EB) spectra generated by the complete absorption of 91Y and 204Tl beta rays in aluminum, copper, tin, and lead are experimentally measured with a multi-channel NaI(Tl) scintillation spectrometer along with a suitable geometrical arrangement. After being corrected for different possible factors, the measured EB distributions are compared with the modified Bethe-Heitler theory. It is observed that except in the case of very light elements, like aluminum, where there is an exact coincidence between theory and experiment, in general, the experimental values are greater than the theoretical ones. This difference increases with increasing photon energy and also with increasing atomic number of the target element, an observation found to compare favorably with most of the earlier findings.