The increasing cost of conventional construction materials has made it impossible to meet the shelter requirements of the teaming population of Nigeria. There is now need for research work aimed at reviewing the use of these conventional materials or providing alternative materials, which are relatively cheap and available. Lateritic soil is cheap, environmentally friendly and abundantly available building material in every part of Nigeria. The effective utilization of laterite as a component in hollow block production depends on the mix proportioning of the various components of laterized sandcrete. In this study, a mathematical model was developed and used to optimize the mix proportion that will produce the maximum compressive strength of laterite/sand hollow blocks using Scheffe’s simplex lattice method. The model was formulated for the materials: water, ordinary Portland cement, sand and laterite, and it compared favourably with the experimental data. This model predicts the compressive strength of laterite/sand hollow blocks when the mix ratios are known and vise versa. The predictions from the model were tested with student’s t-test and found to be adequate at 95% confidence level. The optimum value of compressive strength predicted by this model is 1.88 N/mm2, which corresponds to a mix ratio of 0.45: 1: 2: 2 for water: cement: sand: laterite respectively.