In this study, we report on the experimentally observed phenomenon of ring-like structures formation from chains of magnetic microparticles in magnetoactive elastomers based on magnetic hard powder. In order to find an explanation for the specific macroscopic magnetic properties of composites, microstructural observations on the elastic composite based on a thin layer of magnetic hard particles have been carried out. Particles embedded in such magnetic composites can move inside the matrix with some restrictions and form chain-like structures on being subjected to magnetizing and turn over as first the strength of the external magnetic field decreases and then the polarity of the field switches to opposite. The quantitative parameters of these processes depend on a number of factors including coercivity and remanence of particles, polymer matrix elasticity, and external field intensity. In zero-field, the magnetized particles can assemble into ring-like structures, thus tending to bring the free energy of the overall system to a minimum. The study is primarily aimed to shed a light on understanding the specific magnetic properties of magnetic polymers, such as magnetoactive or magnetorheological elastomers with a magnetic hard filler. Furthermore, the phenomenon of ring-like structures formation can be used for controlled remote patterning of particles in magnetic elastic composite thin films, which is attractive for various applications.