A scroll fluid machine has a stationary scroll having a first end plate and a first spiral wrap projecting from one side of the first end plate. The first spiral wrap has a tip end. A swivel scroll has a second end plate and a second spiral wrap that projects from the one side of the second end plate. The second spiral wrap has a second end tip, and the first and second spiral wraps are engaged with each other. A first thin steel plate is provided on one side of the end plate between the first end plate and the second tip end. A first thin steel plate has a surface side that faces the second tip end. Further, a second thin steel plate is on one side of the second end plate between the second end plate and the first tip end. The second thin steel plate has a surface side that faces the first tip end. Both of the first and second thin steel plates are provided with conformable layers on the surfaces facing the tip ends. The conformable layers comprise a material that is softer than the first and second tip ends so that during operation a gap between the center portion of the tip ends and the opposite scroll end plate does not become too large. A leakage passage is provided in at least one of the thin plates so as to interconnect a central compression chamber formed by the spiral wraps and the outer circumferential chambers.