A heat-sink-attached power-module substrate comprising: one sheet of ceramic substrate; a circuit layer formed from a plurality of small-circuit layers which are bonded on one surface of the ceramic substrate with spacing each other; one sheet of metal layer bonded on the other surface of the ceramic substrate; a power-module substrate provided with the ceramic substrate, the circuit layer and the metal layer; and one sheet of heat sink bonded on the metal layer of the power-module substrate, wherein each of the small-circuit layers has a stacking structure configured from a first layer bonded on the ceramic substrate and a second layer bonded on a surface of the first layer: the metal layer and the first layers are formed from aluminum sheets having a purity of 99.99 mass% or greater: the heat sink and the second layers are formed from aluminum sheets having a purity lower than that of the metal layer and the first layers: characterized in that when a thickness of the second layers is t1 (mm), a sum total-of joined-surface areas of the second layers is A1 (mm 2), yield strength of the second layers at 25°C is σ11 (N/mm 2), and yield strength of the second layers at 200°C is σ12 (N/mm 2); and a thickness of the heat sink is t2 (mm), a joined-surface area of the heat sink is A2 (mm 2), yield strength of the heat sink at 25°C is σ21 (N/mm 2), and yield strength of the heat sink at 200°C is σ22 (N/mm 2), a ratio (t1 × A1 × σ11) / (t2 × A2 × σ21) at 25°C is 0.85 to 1.40 inclusive; and a ratio (t1 × A1 × σ12) / (t2 × A2 × σ22) at 200°C is greater than 1.0 fold but no more than 1.4 fold as the ratio at 25°C. one sheet of ceramic substrate; a circuit layer formed from a plurality of small-circuit layers which are bonded on one surface of the ceramic substrate with spacing each other; one sheet of metal layer bonded on the other surface of the ceramic substrate; a power-module substrate provided with the ceramic substrate, the circuit layer and the metal layer; and one sheet of heat sink bonded on the metal layer of the power-module substrate, wherein each of the small-circuit layers has a stacking structure configured from a first layer bonded on the ceramic substrate and a second layer bonded on a surface of the first layer: the metal layer and the first layers are formed from aluminum sheets having a purity of 99.99 mass% or greater: the heat sink and the second layers are formed from aluminum sheets having a purity lower than that of the metal layer and the first layers: characterized in that when a thickness of the second layers is t1 (mm), a sum total-of joined-surface areas of the second layers is A1 (mm 2), yield strength of the second layers at 25°C is σ11 (N/mm 2), and yield strength of the second layers at 200°C is σ12 (N/mm 2); and a thickness of the heat sink is t2 (mm), a joined-surface area of the heat sink is A2 (mm 2), yield strength of the heat sink at 25°C is σ21 (N/mm 2), and yield strength of the heat sink at 200°C is σ22 (N/mm 2), a ratio (t1 × A1 × σ11) / (t2 × A2 × σ21) at 25°C is 0.85 to 1.40 inclusive; and a ratio (t1 × A1 × σ12) / (t2 × A2 × σ22) at 200°C is greater than 1.0 fold but no more than 1.4 fold as the ratio at 25°C. characterized in that when a thickness of the second layers is t1 (mm), a sum total-of joined-surface areas of the second layers is A1 (mm 2), yield strength of the second layers at 25°C is σ11 (N/mm 2), and yield strength of the second layers at 200°C is σ12 (N/mm 2); and a thickness of the heat sink is t2 (mm), a joined-surface area of the heat sink is A2 (mm 2), yield strength of the heat sink at 25°C is σ21 (N/mm 2), and yield strength of the heat sink at 200°C is σ22 (N/mm 2), a ratio (t1 × A1 × σ11) / (t2 × A2 × σ21) at 25°C is 0.85 to 1.40 inclusive; and a ratio (t1 × A1 × σ12) / (t2 × A2 × σ22) at 200°C is greater than 1.0 fold but no more than 1.4 fold as the ratio at 25°C.