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An animal model was applied to predict genetic merit for Ayrshire milk yield. The model included fixed herdyear- season (32,287) and random herdsire interaction (32,159), permanent environment, animal, and residual effects. Animals evaluated included 119,541 cows with 301,799 records, 5762 sires, and 11,893 dams without records. Genetic groups (36) were defined for unknown parents and parents not contributing ties or records. Groups were defined by sex of parent and by birth year and sex of animal with unknown parent. Evaluations included combinations of these group effects derived from tracing each path in pedigree back to an unknown parent group. Iteration was by Gauss-Seidel for herd-year-season, permanent environment, and herd-sire interaction effects and by second-order Jacobi for animal and genetic group effects. Iteration was conducted without forming mixed model equations; instead one copy of data sorted by herd and sire was read each round. About 3.5 s of central processing unit time on a Cray X-MP/48 was required per round for the complete model; herd-sire interaction contributed .7 s and later lactations, 1.6 s. Large memory requirements were reduced by evaluating most animals in groups of herds including up to 2500 cows. Information for animals with progeny outside their herd group remained in memory throughout iteration. Genetic evaluations by an animal model that includes factors presently in the national evaluation system can be computed with present computer resources. Application to major dairy cattle breeds appears possible.