The axis symmetric analysis method can neither handle initial curved plates nor be used in the optimization of coil shapes because an axis symmetric coil is the only shape to analyze in this method. But the method using some discrete divisions and steps, can overcome these difficulties and show more accurate, reasonable results of temperatures and deflections in flat or curved plates with initial curvature, than those in the axis symmetric analysis method. Traditionally, the coil shape in induction heating is circular shape and it needs the moving process along heating lines. To overcome these, the “long type coil” with some linear parallel coils is proposed. It does not need the moving process along heating lines and reduces the heating process time. The results of experiments are compared with those of simulation.