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 of the hub to the inlet, R2t is a distance in the radial direction from the axis of the hub to the outlet, and Ls is a length of the shroud surface in the direction of the axis 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 of the hub to the side edge front end, R2ta is a distance in the radial direction of each the blades from the axis 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 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 of the hub to the inlet, R2t is a distance in the radial direction from the axis of the hub to the outlet, and Ls is a length of the shroud surface in the direction of the axis 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 of the hub to the side edge front end, R2ta is a distance in the radial direction of each the blades from the axis 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 of the hub.