The given papers present the results of the investigation of physico-mechanical characteristics of fiber-reinforced fine-grained concretes with polyfunctional modifying additives. The methodology of the construction of experimental-statistical models «modifying additives, dispersible fibers – property» to study density at normal humidity conditions, the limit of compressive strength and the limit of tensile strength in bending cement composites is stated . The graphic reflection of the applied polynomial system for every description was a secondary model from seven triangular Gibbs-Roseboom’s diagrams built with the use of the program Statistica 10.0.1011 and fixed at seven points of a bearing triangle with the isolines of maximums of the investigated properties. According to the results of our experimental study, the most optimal complexes additives and dispersed fibers to increase the investigated characteristics of cement composites have been selected.