Abstract: Laterite, a typically red or reddish brown soil found in abundance in the tropics has been used to partially or wholly replace sand in concrete. Resulting laterised concretes are generally known to exhibit low strengths. In this study, the production of high strength laterised concretes using superplasticiser was experimented. Scheffe’s simplex theory based on (6,2) simplex lattice was used to optimize the mix proportions for the crushing strength of high strength laterised concrete produced using Conplast SP 430 superplasticiser (a sulphonated naphthalene formaldehyde admixture). Mathematical models were developed for the mix proportioning of high strength laterised concrete.