<p><b>Context:</b> The accuracy of estimated breeding values (EBVs) is an important metric in genetic evaluation systems in Australia. With reduced costs for DNA genotyping due to advances in molecular technology, more and more animals have been genotyped for EBVs. The rapid increase in genotyped animals has grown beyond the capacity of the current genomic best linear unbiased prediction (GBLUP) method. <b>Aims:</b> This study aimed to implement and evaluate a new single-nucleotide polymorphism (SNP)–BLUP model for the computation of prediction error variances (PEVs) to accommodate the increasing number of genotyped animals in beef and sheep single-step genetic evaluations in Australia. <b>Methods:</b> First, the equivalence of PEV estimates obtained from both GBLUP and SNP-BLUP models was demonstrated. Second, the computing resources required by each model were compared. Third, within the SNP-BLUP model, the PEVs obtained from subsets of SNP were evaluated against those from the complete dataset. Fourth, the new model was tested in the Australian Merino sheep and Angus beef cattle datasets. <b>Key results:</b> The PEVs of genotyped animals calculated from the SNP–BLUP model were equivalent to the PEVs derived from the GBLUP model. The SNP–BLUP model used much less time than did the GBLUP model when the number of genotyped animals was larger than the number of SNPs. Within the SNP–BLUP model, the running time could be further reduced using a subset of SNPs makers, with high correlations (>0.97) observed between the PEVs obtained from the complete dataset and subsets. However, it is important to exercise caution when selecting the size of the subsets in the SNP–BLUP model, as reducing the subset size may result in an increase in the bias of the PEVs. <b>Conclusions:</b> The new SNP-BLUP model for PEV calculation for genotyped animals outperforms the current GBLUP model. A new accuracy program has been developed for the Australian genetic evaluation system which uses much less memory and time to compute accuracies. <b>Implications:</b> The new model has been implemented in routine sheep and beef genetic evaluation systems in Australia. This development ensures that the calculation of accuracies is sustainable, with increasing numbers of animals with genotypes.</p>