Photonic crystals are the materials with an ordered structure, characterized by periodic changes in the refractive index on a scale comparable with emission wavelengths in the visible and nearinfrared range. This periodic structure designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons. The non-existence of propagating EM modes inside the structures at certain frequencies introduces unique optical phenomena such as low-loss-waveguides, omni-directional mirrors and others. The part of the spectrum for which wave propagation is not possible is called the optical band-gap. 1 Photonic crystals provide new opportunities for controlling light beams due to the presence of a band gap in the density of states of the electromagnetic field at given frequency. Adding distortion in the crystal structure allows the creation a variety of devices, such as waveguides, resonators, filters, splitters, etc. In this paper we consider a two-dimensional Barium Strontium Titanate (BST) ferroelectric photonic crystal structure with two-dimensional (2D) varied periodically permittivity. Photonic bandstructures and photonic bandgap maps of 2D BST-based photonic crystals with different cavities size in a different lattice (square or hexagonal) and slab thickness were calculated using the PWE method. The band structure dependence of the different geometry parameters was shown[1]. This paper is relevant because there are very few public sources of information about photonic crystals research based on ferroelectric thin films of BST. This work was supported by Ministry of Education and Science of the Russian Federation.