Designing of multi-component building compositions is usually done by an empirical method, which is a laborious and time-consuming process. The article deals with the method of designing the optimal building mixture composition based on the criterion of minimal costs. In this study, the effect of composition factors (water demand, binder content, fillers and additives) on compressive and flexural strengths of the gypsum-based mortar and the expanded lightweight filler was determined. According to the results of experiments, the corresponding mathematical models of mortar properties were obtained. Such models have made it possible to develop a design methodology for the mixture composition, which uses methods of mathematical programming. It allows obtaining the optimal composition of the construction mixture, which provides the required properties of the mortar at its minimal cost.