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Abstract We develop a model for the radio afterglow of the giant flare of SGR 1806-20 arising due to the interaction of magnetically-dominated cloud, an analogue of Solar Coronal Mass Ejections (CMEs), with the interstellar medium (ISM). The CME is modeled as a spheromak-like configuration. The CME is first advected with the magnetar’s wind and later interacts with the ISM, creating a strong forward shock and complicated backwards exhaust flow. Using three-dimensional magnetohydrodynamic simulations, we study various relative configurations of the magnetic field of the CME with respect to the ISM’s magnetic field. We show that the dynamics of the forward shock mostly follows the Sedov-Taylor blastwave, while the internal structure of the shocked medium is considerably modified by the back flow, creating a multiple shock configuration. We calculate synthetic synchrotron emissivity maps and light curves using two assumptions: (i) magnetic field compression; (ii) amplification of the magnetic field at the shock. We find that models with magnetic field amplification account better for the observed radio emission.