ABSTRACT The study aimed at investigating which of four traits is the most representative of eggshell strength (destructive eggshell thickness measurement, eggshell weight, egg specific gravity, ultrasonic measurement of eggshell thickness) and could be used for selection purposes. To date, investigations focused mostly on pairwise (eggshell strength vs. another eggshell feature) analyses, resulting in two-, maybe three-trait, models when eggshell traits are considered. Since the covariance estimates are also model dependent, we collected five eggshell traits within one analysis, which better reflects what occurs in nature. The eggs were collected from 4571 Rhode Island White and 2426 Rhode Island Red hens. A multiple-trait animal model and the REML method were employed to compute variance components for calculation of heritabilities and genetic correlations between the traits. On average, the highest correlations were found between the destructive measurement and the other quality traits. It is concluded, however, that the ultrasonic eggshell thickness measurement, also with high genetic correlations with the other traits and leaving an egg intact for further handling, can suit best, as an indirect criterion, the selection for eggshell strength.