A synchronous reluctance type rotary electric machine of an embodiment includes a shaft and a rotor core. The shaft rotates around a rotation axis. The rotor core is fixed to the shaft and includes multi-layered hollow parts having a convex shape toward a radially inward side formed for each pole in cross section. Then, when a center in a circumferential direction of one pole is a pole center, a hollow part closest to the shaft among the plurality of hollow parts is a first hollow part, a hollow part positioned next to the first hollow part is a second hollow part, and a hollow part positioned on a side opposite to the first hollow part with respect to the second hollow part is a third hollow part, a width W1 between the first hollow part and the second hollow part on the pole center and a width W2 between the second hollow part and the third hollow part on the pole center are set to satisfy W1≤W2.