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The results of theoretical estimation of capabilities of the material structure modification of 1560 aluminum alloy sheets under processing by severe plastic deformation are presented in this paper. Severe plastic deformation of flat specimens is effected by the constrained groove pressing method in original dies with trapezoidal teeth. The numerical simulation results of the sheet specimen treatment process by severe plastic deformation were used for dies designing. The stress-strain state of flat aluminum alloy specimens and the steel dies at high processing temperature, support reaction force during pressing and the degrees of plastic strain accumulation at the optimum mode of pressing were estimated. The main numerical result is the value of accumulated plastic strain in the specimen per one pressing cycle which is about 1.14. Large degrees of strain are the reasons of grain structure and material texture changes, which leads to inevitable change of its physical-mechanical properties. Increasing the number of pressing cycles leads to proportional increase of the degree of accumulated plastic strain.