Calculating selection and genetic parameters is an important step in improving economically significant genetic traits, particularly in pig breeding. These calculations determine the breeding strategies for assessing the breeding value of animals. This article presents the results of developing linear mixed models to assess variance components and predict breeding values in Yorkshire and Landrace pigs for the following traits: the number of piglets born alive (NBA), the average birth weight (ABW) per, and the average daily weight gain (ADWG) until reaching 100 kg. The effect of fixed factors on the variability of pig productivity traits was analyzed. A nonlinear relationship was revealed between NBA and ABW and the factor “parity number”. Phenotypic and genetic correlations and heritability estimates of the analyzed pig populations’ breeding traits were calculated. The heritability estimates were 0.14, 0.20, and 0.40 for NBA, ABW, and ADWG, respectively, in Yorkshire pigs and 0.13, 0.18, and 0.43, respectively, in Landrace pigs. Negative genetic correlations were found between NBA and ABW (–0.24 and –0.33 for Yorkshire and Landrace pigs, respectively), as well as positive correlations between ABW and ADWG (+0.23 and +0.28 for Yorkshire and Landrace pigs, respectively). These selection and genetic parameters will be used to predict the breeding value of pigs and assess selection indexes in the two breeds.