Investigation of dynamics of self-similarly evolving magnetic clouds Magnetic clouds (MCs) are “magnetized plasma clouds” moving in the solar wind. MCs transport magnetic flux and helicity away from the Sun. These structures are not stationary but experience temporal evolution. Simplified MC models are usually considered. par We investigate the dynamics of more general, radially expanding MCs. They are considered as cylindrically symmetric magnetic structures with low plasma $eta$. par We adopt both a self-similar approach method and a numerical approach. par We demonstrate that the forces are balanced in the considered self-similarly evolving, cylindrically symmetric magnetic structures. Explicit analytical expressions for magnetic field, plasma velocity, density, and pressure within MCs are derived. These solutions are characterized by conserved values of magnetic flux and helicity. We also investigate the dynamics of self-similarly evolving MCs by means of the numerical code Graale. In addition, their expansion in a medium of higher density and higher plasma $eta$ is studied. It is shown that the physical parameters of the MCs maintain their self-similar character throughout their evolution. par After comparing different self-similar and numerical solutions, we are able to conclude that the evolving MCs are quite adequately described by our self-similar solutions -- they retain their self-similar, coherent nature for quite a long time and over large distances from the Sun.