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A mechanical metamaterial is considered using mathematical modeling and computer simulation. Its structure consists of tetrachiral elements providing a non-conventional behavior under uniaxial tension/compression. The deformation behavior of the metamaterial is investigated on its solid computer model using the finite element method. A uniaxial loading of the mechanical metamaterial sample is simulated as a quasistatic problem within the linear elasticity theory. Hooke's law for an isotropic material is chosen as the constitutive equation for the base material. A new method of overlapping is proposed for connecting the unit cells of a three-dimensional metamaterial. It allows achieving the maximum twisting effect. The graphs of dependence of the angle of twist and effective Young's modulus on the parameters characterizing the unit cell structure of the metamaterial are presented. [ABSTRACT FROM AUTHOR]