The first and second weld areas of respective first and second metallic workpieces of aluminum or aluminum alloy are held in abutment against each other with a surface of the second metallic workpiece being positioned on a positioning guide of the first metallic workpiece. A recess is defined between the positioning guide and the second metallic workpiece. A high-density energy beam such as a laser beam is applied to the first and second weld areas thereby to develop a molten pool therein that grows toward the positioning guide until metallic oxide films formed on the first and second metallic workpieces are forced into the recess by the molten pool. As no metallic oxide films are present in a weld joint between the first and second metallic workpieces, the resultant welded structure is of a high mechanical strength.