Ultrasonic testing using a normal incident longitudinal wave is treated for sizing a closed crack. The crack exists vertically on the back wall of a plate inspected. Reflection and transmission of the wave at the closed crack surfaces are analysed by introducing a model of crack closure. The model includes a stress closing the crack and a phase shift of the reflected and trasmitted waves as unknown parameters. The unknown parameters have been determined together with the unknown length of the crack by analysing the inverse problem, which compares the back-wall echo height obtained through both theory and experiment. Two kinds of cracks introduced by different stress ratio in fatigue have been examined. The ultrasonic measurements for specimens have shown that the present analysis offers a powerful tool for precise sizing of closed vertical crack.