Several aspects of the evolution of an SNR into a low-beta ISM are investigated. The presence of a strong magnetic field in the unperturbed ISM is found to have a profound effect on the structure and evolutionary pattern of an SNR embedded in it. If the field strength is high enough for the outgoing shock to be weak, then most of the explosion energy is taken up by the magnetic configuration, and the initial expansion is rapidly braked. There is no adiabatic Sedov phase. When the interstellar Alfven speed is small compared to the ejecta velocity, the initial phases are similar to the nonmagnetic case, except close to the ejecta where a magnetic sheath may form. A tentative application of this study to different objects in the central regions of galaxies where a strong field is present is suggested.