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Progress in developing advanced photonic devices relies on introducing new materials, discovered physical principles, and optimal designs when constructing their components. Optical systems operating on the principles of excitation of extremely high-quality factor trapped modes (also known as the bound states in the continuum, BICs) are of great interest since they allow the implementation of laser and sensor devices with outstanding characteristics. In this paper, we discuss how one can utilize the anisotropic properties of novel materials (transition metal dichalcogenides, TMDs), particularly, the bulk molybdenum disulfide (MoS2), to realize the excitation of trapped modes in dielectric metasurfaces. The bulk MoS2 is a thin-film structure in which the light wave behaves the same way as that in the uniaxial anisotropic material with the form birefringence property. Our metasurface is composed of an array of disk-shaped nanoparticles (resonators) made of the MoS2 material under the assumption that the anisotropy axis of MoS2 can be tilted to the rotation axis of the disks. We perform a detailed analysis of eigenwaves and scattering properties of such anisotropic resonators as well as the spectral features of the metasurface revealing dependence of the excitation conditions of the trapped mode on the anisotropy axis orientation of the MoS2 material used.