The objective of this study was to predict breeding values for single- and multi-trait animal models and compute their reliabilities using a direct inversion method (DIM), and single (ST-APM) and multi-trait approximate methods (MT-APM). Variance and covariance components of lean meat (LM) content, average daily gain (ADG) from birth until the end of the field test, and number of piglets born alive at first (NBA1) and second and subsequent parities (NBA2), were estimated for the analyses of Czech Large White pigs (390,734 records), using single- and four-trait animal models. The average reliabilities estimated by DIM for all considered animals were 0.514 ±0.069, 0.406 ±0.070, 0.050 ±0.044, and 0.321 ±0.090 for LM, ADG, NBA1, and NBA2, respectively. Values of 0.576 ±0.087, 0.150 ±0.078, 0.228 ±0.078, and 0.323 ±0.099, were obtained for the ST-APM for LM, ADG, NBA1, and NBA2, respectively. The use of MT-APM slightly increases the reliability of breeding values by 4%, 6%, 14% and 8% for LM, ADG, NBA1, and NBA2, respectively. In addition, the dependence of the reliability values on the number of offspring of breeding boars is obtained; the reliability increases from 0.215 for less than 5 offspring to 0.989 for more than 400 offspring for the LM trait. Calculated Pearson’s and Spearman’s correlation coefficients between the employed methods were, in general, high, positive, and highly statistically significant. The multi-trait approximation method can be used for the calculation of reliabilities of breeding values as an alternative for direct inversion method that has computational limitations.