A magnetic memory device and a method of manufacturing the same, which are advantageous not only in that both the improvement of storage sensitivity and the reduction of power consumption can be achieved, but also in that a buried wiring having low resistance and high reliability can be formed in reduced time in a stable manner. Soft magnetic material layers forming the cladding structure of a word line and a bit line constituting an MRAM are formed by electroless plating, and the soft magnetic material layers are formed around main wirings (especially copper) of the word line and bit line so that the soft magnetic material layers individually have a uniform, satisfactory thickness, and further they are deposited with improved uniformity on the surface with which the electroless plating solution is in contact, and therefore the uniformity of cladding is improved at not only the bottom surface but also the sidewall of a wiring trench.