Bread wheat is the primary bread crop in the majority of countries in the world. The most important product that is manufactured from its grain and flour is yeast bread. In order to obtain an excellent bread, grain with high physical properties is needed for flour and dough. The Russian spring wheat cultivar Saratovskaya 29 is characterized by its exclusively high physical properties of flour and dough. The purpose of this work was to identify the chromosomes carrying the main loci for these traits in Saratovskaya 29 and to map them using recombinant substitution lines genotyped with molecular markers. A set of inter-varietal substitution lines Saratovskaya 29 (Yanetzkis Probat) was used to identify the “critical” chromosomes. The donor of individual chromosomes is a spring cultivar with average dough strength and tenacity. Substitution of 1D and 4D*7A chromosomes in the genetic background of Saratovskaya 29 resulted in a significant decrease in the physical properties of the dough. Such a deterioration in the case of 1D chromosome might be related to the variability of gluten protein composition. With the help of recombinant substitution double haploid lines obtained from a Saratovskaya 29 (Yanetzkis Probat 4D*7A) substitution line the region on the 4D chromosome was revealed in the strong-flour cultivar Saratovskaya 29, with the microsatellite locus Xgwm0165 to be associated with the unique physical properties of flour and dough. The detected locus is not related to the composition gluten proteins. These locus may be recommended to breeders for the selection of strong-flour cultivars. Additionally, a QTL associated with vitreousness of grain was mapped in the short arm of chromosome 7A.