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Eucalyptus cladocalyx F. Muell is a tree species suitable for low-rainfall sites, even with annual average precipitation as low as 150 mm per year. Its wood is classified as highly durable and its permanence in soil is longer than 25 years, so it can be used for multiple applications. Given that about 41% of the world's land area is classified as drylands, added to the impact of climate change on the availability of water resources, it becomes necessary to use plant species that can tolerate environments with low water availability. In this study, a Bayesian analysis of genetic parameters showed that wood density (WD) was moderately heritable, with a posterior mean of h(2) = 0.29 and a Bayesian credibility region (90%) of 0.06-0.74, while the slenderness coefficient (SC) was highly heritable, with a posterior mean of h(2) = 0.48 and a Bayesian credibility region (90%) of 0.11-0.87. Through Bayesian regression analysis, we identified four and three significant associations for WD and SC, respectively. Another important finding of the bi-trait Bayesian analysis was the detection of three large-effect pleiotropic QTLs located on LG4 at 52 cM, on LG2 at 125 cM, and on LG6 at 81 cM. Bayesian bi-trait regression and the posterior probability of association indicated that three QTLs presented strong evidence of association with WD and SC. This provides convincing evidence that the loci qtlWD130/qtlSC130, qtlWD195/qtlSC195, and qtlWD196/qtlSC196 have a significant pleiotropic effect. The association mapping based on multivariate Bayesian regression was useful for the identification of genomic regions with pleiotropic effects. These loci can be used in molecular marker-assisted breeding to select trees with better wood density.