In this document, we study the behavior of a magnetorheological fluid con-fined in a Hele-Shaw cell subjected to a radial magnetic field. The interface patterns grow due to the action of the external magnetic field, and the inter-facial and yield stress tensions attenuate this growth. Interface patterns are further weighted by viscous effects. The studies aimed to understand the influence of stabilizing factors: yield stress in the absence of a magnetic field and yield stress in the presence of a magnetic field. The basic mathematical concepts necessary to obtain the interface patterns formed between the magnetorheological fluid and the external fluid were approached, in addition to the linear growth rate as a function of the azimuthal number of the dis-turbance through which it was possible to validate the numerical implemen-tation. Performing nonlinear computational simulations through MATLAB software, it was understood how these stabilizing factors influence the behavior of the system and how their influences vary according to the initial conditions. Furthermore, contrary to what the linear theory indicates, the simulations showed a difference in the resulting behavior between the con-stants studied.