We have studied the current‐induced magnetic‐flux structures in type‐I superconducting constrictions using a high‐resolution magneto‐optical method. The samples were Pb films 60–100 &mgr;m thick with a single constriction of 0.5–1.0 mm width, similar to the Anderson‐Dayem bridge geometry. In the resistive state, moving flux‐tube trains are nucleated at both sample edges, at first precisely at the narrowest portion of the constriction. With increasing current, the flux‐tube trains extend more and more into the outlying regions performing a curved path. From the resistive voltage and our magneto‐optical observations the flux‐tube nucleation rate for a flux‐tube train is estimated using the Josephson relation.