We discuss formation of cosmic strings associated with a spontaneously broken approximate U(1) symmetry by performing classical field-theoretical simulations. An original U(1) symmetry is explicitly broken down to its subgroup Z_N even before spontaneous breaking takes place. We estimate the ratio of explicit breaking to that of spontaneous breaking for which topological defects for N=1 and N=2 are formed. For N=1, a cosmic string attached to a single domain wall can be formed when the amount of the explicit breaking is 3 orders of magnitude smaller than that of the spontaneous breaking. For N=2, no matter how large the explicit breaking is, domain walls are inevitably formed as long as the temperature of the Universe is high enough to restore Z_2 symmetry. In that case, cosmic strings are also inevitably formed as long as the amount of the explicit breaking is smaller than that of the spontaneous breaking.


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