The Elston-Stewart algorithm for a normally distributed trait under a polygenic model is explained in detail and extended to allow for other continuous environmental variables. This formulation is especially useful for large pedigrees, as it avoids the need to invert matrices. Whereas it may not be feasible by this method to estimate all the various components of previously suggested models for polygenic inheritance, it can allow for a reasonably flexible pedigree correlational structure under which valid tests can be performed for fixed effects that may affect the phenotype.