Nanostructures of high-refractive-index materials such as semiconductors can support Mie resonances due to confinement of light at the nanoscale and have been investigated both theoretically and experimentally for a range of nanophotonic applications. Transition metal dichalcogenides (TMDCs) from the family of van der Waals layered materials have high refractive index and strong optical anisotropy. Recently, it has been shown that due to the tunable optical properties of TMDCs, they possess enormous potential for designing metasurfaces and various ultra-thin optical elements. Periodically arranged nanoantennas of van der Waals layered materials can exhibit strong spectral resonances in the visible and near-infrared frequencies. In this work, we investigate the scattering and transmission properties of a periodic array of disk-shaped nanoantennas of a TMDC material, tungsten disulfide WS2. We show the dependence of the reflection and transmission spectra from the TMDC nanoantenna array and investigate the spectral features for various thicknesses of the supporting layers positioned between the antenna array and glass substrate.