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With the fast development of ultrashort pulse laser sources, the classic Gaussian beam has become a bottleneck for faster and more efficient micromachining of transparent materials. Its relatively short focal zone is not suitable for efficient microchannel creation in various glasses, therefore the Bessel beam is a great alternative for that, because of its elongated focal line. One of the most common optical elements for such beam generation is an axicon-conical lens with a sharp tip at the center that can be either refractive or diffractive. However, these beam generation methods have disadvantages, such as the complex manufacturing of an ideal surface of axicons. There also exist alternative ways of producing nondiffracting beams by geometrical phase elements. Such optical elements consist of polarization-sensitive volume nanogratings, which can have unique and complex patterns for the manipulation of incoming light. This work aims to familiarize with the formation and control of invariant, Bessel type beams by using geometric phase elements. The results of numerical simulation and experimental data are presented where controllable phase shifts are induced in axicon mask, therefore new and unique invariant beams are generated. The main results and conclusions: 1. Numerical simulations of beam propagation behind phase-shifted diffractive elements have similar properties to the Bessel beam. Beam propagation simulations provided in this work are particularly close to experimental results, small deviations could be caused by optical schemes or elements irregularities. 2. Demonstrated phase-shifted axicons produced as geometric phase elements, which could be reliable for various invariant beam formation, due to high threshold and efficiency (93 - 94 %), also it is a good alternative for complex phase mask processing. 3. Geometric phase elements could be reliable for invariant beam formation and high power laser micromachining: was demonstrated borosilicate glass modification by using two different invariant beams. One of them was used for controllable microcracks formation in the transparent material and producing laser dicing technology with high diced wall quality, 0.2 μm roughness was achieved.