Allogeneic bone marrow transplantation (allo-BMT) is currently the only way to cure many hematoproliferative disorders. However, allo-BMT use is limited by severe complications, the foremost being graft-versus-host disease (GVHD). Due to the lack of efficiency of the existing methods of GVHD prophylaxis, new methods are being actively explored, including the use of donors' multipotent mesenchymal stromal cells (MMSC). In this work, we analyzed the results of acute GVHD (aGVHD) prophylaxis by means of MMSC injections after allo-BMT in patients with hematological malignancies. The study included 77 patients. They were randomized into two groups - those receiving standard prophylaxis of aGVHD and those who were additionally infused with MMSC derived from the bone marrow of hematopoietic stem cell donors. We found that the infusion of MMSC halves the incidence of aGVHD and increases the overall survival of patients. Four of 39 MMSC samples were ineffective for preventing aGVHD. Analysis of individual donor characteristics (gender, age, body mass index) and the MMSC properties of these donors (growth parameters, level of expression of 30 genes involved in proliferation, differentiation, and immunomodulation) revealed no significant difference between the MMSC that were effective or ineffective for preventing aGVHD. We used multiple logistic regression to establish a combination of features that characterize the most suitable MMSC samples for the prevention of aGVHD. A model predicting MMSC sample success for aGVHD prophylaxis was constructed. Significant model parameters were increased relative expression of the FGFR1 gene in combination with reduced expression levels of the PPARG and IGF1 genes. Depending on the chosen margin for probability of successful application of MMSC, this model correctly predicts the outcome of the use of MMSC in 82-94% of cases. The proposed model of prospective evaluation of the effectiveness of MMSC samples will enable prevention of the development of aGVHD in the maximal number of patients.