A turbine , comprising: a housing including an inlet , an outlet , and a shroud section having a shroud surface extending between the inlet and the outlet ; and a turbine impeller housed in the housing and including a hub and a plurality of blades disposed on an outer peripheral surface of the hub , each of the blades having a side edge extending along the shroud surface , wherein the side edge of each of the blades has a side-edge upstream portion disposed on a side of the inlet , and a side-edge downstream portion disposed on a side of the outlet , wherein the shroud surface has a shroud upstream portion disposed on the side of the inlet and extending along the side-edge upstream portion , and a shroud downstream portion disposed on the side of the outlet and extending along the side-edge downstream portion , characterized in that the shroud upstream portion has a meridional cross-sectional shape having a curvature radius R defined by following expression 1: R ≧ R 1 − R 2 t 2 + Ls 2 2 R 1 − R 2 t where Ri is a distance in a radial direction from the axis (L) of the hub to the inlet , R2t is a distance in the radial direction from the axis (L) of the hub to the outlet , and Ls is a length of the shroud surface in the direction of the axis (L) of the hub , and in that the side-edge upstream portion of each the blades has a meridional cross-sectional shape having a curvature radius Ra defined by following expression 2: Ra ≧ R 1 a − R 2 ta 2 + Lsa 2 2 R 1 a − R 2 ta where R1a is a distance in the radial direction of each the blades from the axis (L) of the hub to the side edge front end , R2ta is a distance in the radial direction of each the blades from the axis (L) of the hub to the side-edge rear end , and Lsa is a length of the side edge of each the blades in the direction of the axis (L) of the hub . a housing including an inlet , an outlet , and a shroud section having a shroud surface extending between the inlet and the outlet ; and a turbine impeller housed in the housing and including a hub and a plurality of blades disposed on an outer peripheral surface of the hub , each of the blades having a side edge extending along the shroud surface , wherein the side edge of each of the blades has a side-edge upstream portion disposed on a side of the inlet , and a side-edge downstream portion disposed on a side of the outlet , wherein the shroud surface has a shroud upstream portion disposed on the side of the inlet and extending along the side-edge upstream portion , and a shroud downstream portion disposed on the side of the outlet and extending along the side-edge downstream portion , characterized in that the shroud upstream portion has a meridional cross-sectional shape having a curvature radius R defined by following expression 1: R ≧ R 1 − R 2 t 2 + Ls 2 2 R 1 − R 2 t where Ri is a distance in a radial direction from the axis (L) of the hub to the inlet , R2t is a distance in the radial direction from the axis (L) of the hub to the outlet , and Ls is a length of the shroud surface in the direction of the axis (L) of the hub , and in that the side-edge upstream portion of each the blades has a meridional cross-sectional shape having a curvature radius Ra defined by following expression 2: Ra ≧ R 1 a − R 2 ta 2 + Lsa 2 2 R 1 a − R 2 ta where R1a is a distance in the radial direction of each the blades from the axis (L) of the hub to the side edge front end , R2ta is a distance in the radial direction of each the blades from the axis (L) of the hub to the side-edge rear end , and Lsa is a length of the side edge of each the blades in the direction of the axis (L) of the hub . <EOS>