This article contains the results of work on the development of the brilliant idea of James Clerk Maxwell that elementary particles are vortices of material substance that fills our entire Universe. He considered the main problem of this idea to be the impossibility of keeping the vortices from disintegrating into a chaotic (thermal) motion of the particles of the medium. It was possible to develop a model in which certain simple processes constantly carried out in a liquid make it possible to keep vortices in this liquid indefinitely. Model studies have shown that the processes that allow keeping vortices in liquids endow these vortices with all analogues of the fundamental physical properties that real elementary particles have. The developed model clearly explains: what is the spin of a particle, what is the rest energy of a particle, how particles create fields, how forces arise and what connects all fundamental interactions (forces) with each other, why a particle behaves like a wave, why a liquid in which and there are vortices-particles perceived by them as "emptiness" and much more. In addition, the model has a speed limit similar to the speed of light and analogs of space and time. The model can be tested experimentally. Methods for experimental verification of the model are proposed.