We demonstrated and investigated, both theoretically and experimentally, the transformation of cylindrical vector beams with an embedded phase singularity under the condition of focusing perpendicularly to the axis of the anisotropic calcite crystal. Theoretical and numerical analysis, performed on the basis of decomposing the light field into a set of plane waves for an anisotropic medium, allowed us to study the dependence of the structural transformation of the initial laser beam on the polarisation and phase state in detail. the proposed approach allows one to perform the visual recognition of cylindrically-polarised vector beams of various orders and can be used for the demultiplexing of information channels in the case of polarisation-division multiplexing. The experimentally-obtained results agree with the theoretical findings and demonstrate the reliability of the approach. Nonparaxial propagation of laser modes in a medium with strong anisotropy leads to complex polarisation-phase transformations 1-3 , which allow for the formation of inhomogeneously polarised beams 4-9 , as well as beams with vortex phase singularities 10-13. In the latter case, it is possible to observe the transformation of the initial circularly-polarised beam with non-zero spin angular momentum into a laser beam with non-zero orbital angular momentum. These effects can also be produced by focusing laser radiation along the axis of an anisotropic crystal, due to the interaction of the ordinary and extraordinary beams 14. When laser beams propagate perpendicularly to the crystal axis 2,3,15-22 , various effects are observed. In particular, for Bessel beams, pronounced astigmatic distortion of the ring structure of the beam occurs 3,18,21,22. For Gaussian beams, the astigmatic transformation is hardly noticeable 23 , since natural crystals, as a rule, have a slight relative difference between the ordinary and extraordinary refractive indices. To enhance the astigmatic transformation and make it visually noticeable, sharply focused vortex Gaussian beams are used. In this case, the influence of the polarisation of the illuminating beam becomes especially important 24. In the present paper, the variable transformation of singular cylindrical vector beams (CVBs) 25-27 using an anisotropic crystal is investigated theoretically, numerically, and experimentally. In order to introduce into the initial CVB a complex singular phase of superposition of optical vortices, we used a spatial light modulator (SLM). Earlier, SLMs were also used for modification of incident laser radiation and the generation of amplitude-squeezed high-order vector beams by means of a collinear interferometric technique 28. Because of the use of the SLM, the vortex composition and the weight ratio in this superposition can change dynamically. Following this, when the generated field is focused perpendicularly to the axis of an anisotropic crystal, a selective (polarisation-dependent) astigmatic transformation of the individual components of the electric field occurs. Thi...