Stress in farrowing sows is associated with the number of piglets crushed or attacked. Sow’s behaviour is variable and heritable, therefore genetic selection can be a viable approach for improving pig’s welfare. In this report, we used first parity litter records of Yorkshire sows to test a genetic evaluation model for piglet crushing. The data were split into training and validation to check the prediction accuracy of piglet crushing estimated breeding values (EBVs) for young sows. We found that the estimated heritability of piglet crushing was 0.07 ± 0.03. The difference in the EBVs in the validation set was equivalent to 0.15 more piglets crushed in the top 10% group than in the bottom group of sows. These results indicate that the genetic selection may be used to reduce piglet crushing which will improve the welfare of pigs as well as production efficiency. The average reliability of the estimated EBVs across all animals in the pedigree was (0.07; 0.0 to 0.72). More research on evaluation models and the genetics underlying sow stress and behaviour is warranted to improve the reliabilities of modeling and to identify robust genetic markers for animal breeding for the implementation.