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Metasurfaces are artificial structures based on the subwavelength resonant particles that allow to control the amplitude, phase, frequency, polarization state and angular momentum of electromagnetic waves in a desired way. In this report, we demonstrate how one can utilize the anisotropic properties of bulk molybdenum disulfide (MoS2), to achieve the excitation of trapped modes (also known as the bound states in the continuum, BICs) in all-dielectric metasurfaces. Bulk MoS2 is a novel material that is characterized by a thin-film structure. The electromagnetic waves interact with this media in the same way as with in the uniaxial anisotropic material possessing the form birefringence property. Studied metasurface is composed of disk-shaped resonant nanoparticles made of the MoS2 material arranged in two-dimensional array. We assume that the anisotropy axis of MoS2 can be tilted to the rotation axis of the disks. A detailed analysis of scattering characteristics and eigenwaves of such anisotropic resonant nanoparticles as well as the spectral behaviors of the metasurface, is carried out, revealing dependence of the conditions for excitation of the trapped mode on the orientation of the anisotropy axis of the MoS2 material used.