Eucalyptus tereticornis is a species with technological characteristics which make it potentially adequate to be planted for industrial purposes in Santiago del Estero, Argentina. To prove adaptation in this area and to improve growth and form traits, 51 open-pollinated families were planted in Santiago del Estero. The trial was laid out in a Randomized Complete Block design with four replications and five-tree plots. At 10th year, the stem straightness and diameter at 1.30-meter height were assessed to evaluate families for backward selection. Variance components were estimated by Restricted Maximum Likelihood (REML) and breeding values predicted using Best Linear Unbiased Prediction (BLUP). Estimations of the genetics parameters for diameter and stem straightness showed, respectively, family heritability of 0.57 and 0.49 and genetics gains of 4.55 % and 3.79 %. Genetic correlation between traits was low (- 0.05). This result allows independent improving in both traits.