Growth, carcass and tenderness data from 415 Polled Nellore animals were analyzed in order to estimate the genetic correlations between tenderness (WBSF) and growth (ILW, FLW and ADG) and carcass (BF, RF and LMA) traits. The covariance components and genetic parameters were estimated using the Gibbs Sampling method. The heritability estimated for WBSF was of low magnitude (0.11 ± 0.022). The genetic correlations between WBSF and the other traits were of low magnitude, with values of - 0.15; -0.18; -0.13; 0.10; -0.12 and 0.18, between WBSF and ILW, FLW, ADG, BF, RF and LMA, respectively. The results support the conclusion that selection for improved tenderness will not affect genetic progress in other economic traits and vice-versa, but more studies are required for a better knowledge of the genetic relationships between meat tenderness and other traits for Polled Nellore cattle