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This paper presents an investigation of terajets formation by dielectric periodic structure at terahertz frequencies (0.1–0.2 THz) in effective medium regime (photonic metamaterial). The dispersions of effective permittivity for periodic structures formed by plastics (ABS, black) were analytically obtained for both regimes. The study of the interaction of a plane wave and artificial cubic dielectric on a substrate parallelepiped to form a subwavelength terahertz beams (terajet) was performed. The results of numerical simulation of S-parameters of structure are discussed. The subwavelength beam waist of terajets about 0.39?–0.41? were obtained. The quality factor of terajets are discussed. The results may be applied for creation of methods to obtain subwavelength beams in the terahertz frequency range, and devices based on them. These investigations are opening new research lines such as mesoscale focusing devices for different sensing applications.