This paper describes the derivation of two production functions showing the dependence of maize grain yields on fertilization and rainfall. The data were taken from maize fertilizer trials conducted for eleven years at the Dundee Research Station. The mbdels lend themselves to economic analysis. Fertilization was represented by either applied nitrogen (N) and applied phosphate (Pa) or N and post fertilization P soil test (Pt) readings. The functions conform to the Law of Diminishing . 1.eturns, and show a- positive interidion-between the two nutrients. Total rainfall was determined for a pre-planting period and a sequence of consecutive growth stages, extending from sowing to physiological maturity. The models include linear rainfall terms and linear rainfall-nutrient interaction terms. The adjusted R2 values were 0,897 for the model using P applied, and 0,805 for the P soil test model.