Materials with a through porosity occupy a special place in dental implantology. Nikelid titanium obtained by the method of self-propagating high-temperature synthesis (SHS) is characterized by the phase heterogeneity (the secondary phases Ti2Ni and TiNi3 are present in large numbers along with the main phase TiNi). One of the alternatives for this material is the nonvowen titanium material with a through porosity (MR), representing the elastically deformed system. In this research we investigated the deflected modes of the system “MR-bone”. Deflected mode was studied using the Belousov-Troynikov’s mathematical model and the finite element method. The maximum stress of the nonvowen titanium material with a through porosity was 367 kPa. The stress on the walls of the bone bed was 105 kPa, while the stress of the titanium sleeve with identical dimensions - 394 HPa and stress on the walls of the bone bed was 100 HPa, that exceeds the strength of modern materials in dozens of times. The results of this research determine the prospect of application of the nonwoven titanium material with a through porosity in medicine.