Rayleigh-Brillouin scattering measurements have been conducted on a thoriated fluoride and a fluorozirconate glass. Values of the elastic and photoelastic constants of these glasses pertaining to the longitudinal and transverse acoustic modes have been determined. In addition, corrections due to absorption have been explicitly included in the calculation of the photoelastic constants. We note that although fluoride glasses of similar compositions have been previously measured, little or no data on the transverse Brillouin components have been reported, while values of C44 and P44, have been determined for both fluoride glasses in our study. Additional results on the Rayleigh scattering losses have also been obtained and indicate smaller scattering losses from the fluorozirconate glass than from the thoriated fluoride glass.