Best linear unbiased prediction (BLUP) is a powerful method to estimate genetic values of animals, and is widely applied in many animal species but poultry. Beijing White Leghorn nested data in 1986-1987 with 777 individuals were analysed by animal model and multiple trait BLUP. Two traits (40-week egg production and 36-week egg weight) and two fixed effects (house-pen effect and hatching batch effect) were considered. The way to calculate a large set of mixed model equations in micro-computer was studied. Only non-zero elements of the coefficient matrix of MME were stored on a disk. The iteration process was reduced by block iteration. It also simplified the multiple trait BLUP method, the dimension of equations is only 1/q (q is the number of traits) of regular method. So it saved a lot of compute time and cost, and BLUP became applicable in poultry. The significance of using BLUP in poultry are: (1) Eliminating some fixed effects; (2) Reducing the estimation error for unbalanced data; (3) Estimating breeding values of progeny, so we can shorten the generation interval; (4) It can estimate breeding values of individuals without records from the relatives' information; (5) The breeding value of sires and dams can be estimated from their progeny records, used for family selection; (6) Due to genetic and environmental correlation between traits and all relatives information were considered, it can increase the selection accuracy.