This work aims at assessing the suitability of runoff sand for concrete production and presents Simplex Lattice Design models for the determination of Modulus of Rupture of Concrete. Fine aggregates obtained from five different sources tagged Samples A, B, C, D and E were used to produce concrete beams referred to as Concrete A, Concrete B, Concrete C, Concrete D and Concrete E respectively. Two of the fine aggregate samples were obtained from Otamiri and Njaba rivers while the other three samples were runoff sand from Awomama, Iho and Nekede (all in Imo State, Nigeria). Each fine aggregate sample was used to produce sixty concrete beam specimens which were tested for modulus of rupture giving a total of 300 concrete beams measuring 150 x 150 x 600, mm in dimension. Scheffe's simplex lattice design technique was used to formulate mathematical models for the determination of the modulus of rupture of the produced concrete beam specimens. The values of responses determined from the models agreed with the corresponding values obtained experimentally. The formulated models can predict all possible combinations of mix proportions if the value of modulus of rupture is given. Conversely, it can determine the modulus of rupture if a mix proportion is specified. The formulated models were tested for adequacy using Fstatistic test. The models were found to be adequate. The highest optimum modulus of rupture predictable within the factor space of Scheffe's Simplex lattice design models is 9.99 N/mm 2 obtained from Sample D.