Elastic properties of uniaxial ferroelectric strontium barium niobate, SrxBa1-xNb2O6 (SBN100x), crystals were studied by Brillouin scattering. With the increase of x, the random fields (RFs) strength becomes strong and the relaxor ferroelectric nature is enhanced. SBN26 (x = 0.26) with very weak RFs undergoes a normal ferroelectric phase transition at the Curie temperature, TC = 464 K. On cooling from a high temperature, the sound velocity of the longitudinal acoustic mode along the ferroelectric c-axis shows a remarkable softening towards TC. The sound attenuation of this mode increases markedly towards TC. These temperature dependences are well fitted by power laws above TC. The relaxation time of a central peak (CP) shows the critical slowing down towards TC. In contrast, SBN80 (x = 0.80) with strong RFs shows only a diffusive elastic anomaly in the vicinity of TC = 289 K and the temperature dependence of a CP is very small. These differences between the observed results of SBN26 and SBN80 can be attributed to the difference of RFs strength.