With the growing emphasis on sustainability, the construction industry is more interested in applying environmental friendly concrete in its construction projects. This paper developed model for predicting the 28th day flexural strength of laterite-quarry dust concrete using (5, 2) extreme vertices design of Minitab 17. Physical property test were conducted on the laterite and quarry dust and several trial mixes of concrete were carried out to determine the lower (Li) and upper bound (Ui) limit of each of the components. River sand was replaced with a maximum of 40% laterite and 60% quarry dust in the trial mixes. Several mix proportions were generated using the extreme vertices design. The design matrix consisted of fifteen (15) design points and seven (7) check points with replications of the vertices and the centroid, given a total of twenty eight (28) runs. Eighty four (84) numbers of laterite-quarry dust concrete beams of 600 x 150 x 150mm were prepared and tested for their flexural strength after 28 days of curing. A second degree polynomial was fitted to the data of the flexural strength test result and adequacy of the model was confirmed using the p-value, F statistics and normal probability plot. Several mix proportions were generated and their flexural strength obtained using the developed model. The minimum and maximum flexural strength predictable by the model are 2.44N/mm2 and 4.95N/mm2. The model can help predict the flexural strength of laterite-quarry dust concrete for both reinforced and non-reinforced concrete design for domestic and commercial constructions.