In the present study, for the first time, a new method for the synthesis of MAX phases of the composition Ti₃SiC₂, combining high-temperature sintering and hot pressing, was proposed and implemented, and this made it possible to obtain the purest material with a Ti₃SiC₂ phase content equal to 99.2%. The Ti₃SiC₂ MAX phases are extremely promising materials for protection of containers and fuel cladding of nuclear reactors taking into consideration their high values of mechanical properties and the unique ability of successful radiation resistance. According to this task, the synthesis methods and formation conditions of the Ti₃SiC₂ MAX phases are considered in the present study involving the following approaches. Among them the second was used for the first time. Various mixtures from initial powders Ti/Si/C, Ti/Si/TiC, Ti/SiC/C and Ti/SiC/TiC were used to synthesize ternary titanium-silicon carbide (Ti₃SiC₂) by sintering followed by hot pressing. The powder Ti/SiС/TiC is the best among all powder mixtures for synthesis Ti₃SiC₂. The relative density of the samples synthesized and consolidated by the hot pressing method reaches 99.4%. It is shown that practically single-phase Ti₃SiC₂consists of elongated laminar grains. The influence of time and temperature of sintering on the formation of the MAX-phase Ti₃SiC₂ from original powders Ti/Si/C was determined. Titanium carbide, as an intermediate phase, is always present in final products. Excess silicon contributes to the greatest phase formation Ti₃SiC₂. The high content of the Ti₃SiC₂ phase in the samples makes it possible to predict their high mechanical properties and resistance to radiation, as well as to consider these materials as the most promising for the further protection of containers and casings of fuel elements of nuclear reactors.