A power-module substrate with heat-sink, comprising: a power-module substrate in which a circuit layer made of copper or a copper alloy is disposed on one surface of a ceramic board and a metal layer is disposed on the other surface of the ceramic board; and a heat sink which is bonded on the metal layer of the power-module substrate and formed from an aluminum-impregnated silicon carbide porous body in which aluminum or an aluminum alloy is impregnated in a porous body made of silicon carbide, wherein where yield stress of the circuit layer is σ1 (MPa), a thickness of the circuit layer is t1 (mm), and a bonding area between the circuit layer and the ceramic board is A1 (mm 2) and yield stress of the metal layer is σ2 (MPa), a thickness of the metal layer is t2 (mm), and a bonding area between the metal layer and the ceramic board is A2 (mm 2); wherein the thickness t1 is formed to be not less than 0.1 mm and not more than 3.0 mm, the thickness t2 is formed to be not less than 0.15 mm and not more than 5.0 mm and the thickness t2 is formed to be larger than the thickness t1, and characterized in that the metal layer is made of copper or a copper alloy; and a ratio {(σ2 × t2 × A2) / (σ1 × t1 × A1)} is in a range not less than 1.5 and not more than 15, wherein, on a lower surface of the heat sink, a center position of a bonding surface between the heat sink and the metal layer is set to be a center of a measuring area, a maximum length of the measuring area is set to L (mm), a deformation amount of the heat sink in the measuring area is set to Z (mm), a warp (Z/L 2) when heated to 285°C is set to X, and a warp (Z/L 2) when cooled to 30°C after heating to 285°C is set to Y, wherein a difference (Y - X) between the warp X and the warp Y is not less than -18.0 × 10 -6 (mm -1) and not more than 18.0 × 10 -6 (mm -1). a power-module substrate in which a circuit layer made of copper or a copper alloy is disposed on one surface of a ceramic board and a metal layer is disposed on the other surface of the ceramic board; and a heat sink which is bonded on the metal layer of the power-module substrate and formed from an aluminum-impregnated silicon carbide porous body in which aluminum or an aluminum alloy is impregnated in a porous body made of silicon carbide, wherein where yield stress of the circuit layer is σ1 (MPa), a thickness of the circuit layer is t1 (mm), and a bonding area between the circuit layer and the ceramic board is A1 (mm 2) and yield stress of the metal layer is σ2 (MPa), a thickness of the metal layer is t2 (mm), and a bonding area between the metal layer and the ceramic board is A2 (mm 2); wherein the thickness t1 is formed to be not less than 0.1 mm and not more than 3.0 mm, the thickness t2 is formed to be not less than 0.15 mm and not more than 5.0 mm and the thickness t2 is formed to be larger than the thickness t1, and characterized in that the metal layer is made of copper or a copper alloy; and a ratio {(σ2 × t2 × A2) / (σ1 × t1 × A1)} is in a range not less than 1.5 and not more than 15, wherein, on a lower surface of the heat sink, a center position of a bonding surface between the heat sink and the metal layer is set to be a center of a measuring area, a maximum length of the measuring area is set to L (mm), a deformation amount of the heat sink in the measuring area is set to Z (mm), a warp (Z/L 2) when heated to 285°C is set to X, and a warp (Z/L 2) when cooled to 30°C after heating to 285°C is set to Y, wherein a difference (Y - X) between the warp X and the warp Y is not less than -18.0 × 10 -6 (mm -1) and not more than 18.0 × 10 -6 (mm -1).