The deterioration of concrete structures is a major problem in many countries throughout the world. This has prompted the search for methods of predicting the service life of both existing and new structure. The present work submits results of experiments evaluating the mechanical properties of portland cement (PC), silica fame (SF) and blast furnace slag (BFS) concrete mixes. In this paper, the Taguchi method has been used to determine optimum conditions for some properties of concretes prepared with SF and BFS by weight of cement under different curing regimes. At first, all the concrete specimens were cured up to 14 days in lime saturated water at 23 +/- 2 degreesC. Afterwards, the concrete specimens were subjected to prepared cure regimes up to experimental days. Chosen experimental parameters were mineral admixture, water-binder ratio, cure regime and cure time. The optimum conditions were found to be mineral admixture 5%SF + 10%BFS, water-binder 0.30, best cure regime lime saturated water, and cure time 28-days.