A scroll type fluid displacement apparatus is disclosed which includes a pair of scrolls each having a circular end plate and spiral element extending therefrom. The scrolls are maintained at an angular and radial offset so that both spiral elements interfit to form a plurality of line contacts to define at least one pair of sealed off fluid pockets. Upon relative orbital motion of the scrolls, the line contacts shift along the spiral curved surfaces of the spiral elements to thereby change the volume of the fluid pockets. In particular, according to the present invention, the thickness of the spiral element of the orbiting scroll is gradually from the inner end of the spiral element to its outer end to increase the mechanical strength of the spiral element at its central portion while avoiding an increase in the centrifugal force generated by the orbiting scroll during orbital motion. On the other hand, the thickness of the spiral element of the other scroll, i.e., the fixed scroll, is gradually increased from the inner end of the spiral element to its outer end to compensate for the change in shape of the facing spiral element of the orbiting scroll.