A permanent magnet embedded rotor for a rotating electric machine, the rotor comprising: a rotor core having a pair of accommodating recesses (21A, 21B) adjacently located with a bridge portion arranged between the accommodating recesses (21A, 21B); and a pair of permanent magnets (17A, 17B) accommodated in the corresponding accommodating recesses (21A, 21B), the permanent magnets (17A, 17B) each having a magnetic pole surface (170A, 170B), a magnetic pole facing surface (191A, 191B) facing each of the magnetic pole surfaces (170A, 170B), wherein the rotor core has a rotor outer circumferential surface as an outer circumferential surface, a d-axis and a q-axis defined in the rotor, each of the accommodating recesses (21A, 21B) has a magnet accommodating portion (19A, 19B) for accommodating the corresponding permanent magnet (17A, 17B) and a cavity (20A, 20B) at the q-axis side of the magnet accommodating portion (19A, 19B), the cavities (20A, 20B) open in the rotor outer circumferential surface, the d-axis side of each of the cavities (20A, 20B) is formed by an outer cavity forming surface (201A, 201B), a starting point (Pa1, Pb1) of each of the outer cavity forming surfaces (201A, 201B) is located on the rotor outer circumferential surface, the outer cavity forming surfaces (201A, 201B) each intersect the corresponding magnetic pole surface (170A, 170B), the rotor outer circumferential surface includes a portion of an imaginary annular line, and the starting points (Pa1, Pb1) of the outer cavity forming surfaces (201A, 201B) are each located between the d-axis and an intersection point (Qa, Qb) between the imaginary annular line and an imaginary extended plane (23A, 23B) of the corresponding magnetic pole facing surface (191A, 191B) that faces the corresponding magnetic pole surface (170A, 170B), characterized in that an end point of each of the outer cavity forming surfaces (201A6, 201B6; 201A7, 201B7) is located on the corresponding magnetic pole facing surface (191A, 191B), and an end portion (172A, 172B) of each magnetic pole surface close to the q-axis is exposed to the corresponding cavity (20A, 20B). a rotor core having a pair of accommodating recesses (21A, 21B) adjacently located with a bridge portion arranged between the accommodating recesses (21A, 21B); and a pair of permanent magnets (17A, 17B) accommodated in the corresponding accommodating recesses (21A, 21B), the permanent magnets (17A, 17B) each having a magnetic pole surface (170A, 170B), a magnetic pole facing surface (191A, 191B) facing each of the magnetic pole surfaces (170A, 170B), wherein the rotor core has a rotor outer circumferential surface as an outer circumferential surface, a d-axis and a q-axis defined in the rotor, each of the accommodating recesses (21A, 21B) has a magnet accommodating portion (19A, 19B) for accommodating the corresponding permanent magnet (17A, 17B) and a cavity (20A, 20B) at the q-axis side of the magnet accommodating portion (19A, 19B), the cavities (20A, 20B) open in the rotor outer circumferential surface, the d-axis side of each of the cavities (20A, 20B) is formed by an outer cavity forming surface (201A, 201B), a starting point (Pa1, Pb1) of each of the outer cavity forming surfaces (201A, 201B) is located on the rotor outer circumferential surface, the outer cavity forming surfaces (201A, 201B) each intersect the corresponding magnetic pole surface (170A, 170B), the rotor outer circumferential surface includes a portion of an imaginary annular line, and the starting points (Pa1, Pb1) of the outer cavity forming surfaces (201A, 201B) are each located between the d-axis and an intersection point (Qa, Qb) between the imaginary annular line and an imaginary extended plane (23A, 23B) of the corresponding magnetic pole facing surface (191A, 191B) that faces the corresponding magnetic pole surface (170A, 170B), characterized in that an end point of each of the outer cavity forming surfaces (201A6, 201B6; 201A7, 201B7) is located on the corresponding magnetic pole facing surface (191A, 191B), and an end portion (172A, 172B) of each magnetic pole surface close to the q-axis is exposed to the corresponding cavity (20A, 20B).