This paper reports the development of a two dimensional mathematical model for the California Bearing Ratio (CBR) of a typical sub base material in terms of the density and moisture to replace the hitherto graphical model of an iso-CBR plot. Conventional laboratory compaction and CBR tests were simultaneously conducted on samples of soils obtained from the highway borrow pits around Ilorin township according to relevant portions of the British standard testing procedure; BS 1377: 1990. The outcomes of the test were used for the formulation of the relationships of the CBR with the resultant of the vectorially combined normalized dry density and moisture content at low compactive and medium compactive energy levels (LCE and MCE). The most efficient forms of the models for the samples from 0-1m and 1-2 m depths below the ground surface are the quadratic and third order equations, with the R² values of more than 90 %. Indeed the differentials of the quadratic model proved that the maximum CBR occurs at Π value of which is the actual indication of the optimum condition when the two normalized parameters are each equal to unity, their maximum values.