A midsole structure of a sole assembly for a shoe improves a ride feeling and stability of the midfoot portion of the sole assembly during running. The sole assembly 1 of the shoe includes an upper plate 3 disposed on an upper side of a midfoot portion M and formed of a hard elastic member, a lower plate 4 disposed under the upper plate 3, wherein the lower plate is formed of a hard elastic member and has a downwardly convexedly curved shape that forms a void S relative to the upper plate, a midfoot outsole 6 attached on a bottom surface 4a of the lower plate 4, having a ground contact surface 6a, and provided discretely in the longitudinal direction from an outsole 5 of a heel portion H and an outsole 7 of a forefoot portion F of the sole assembly 1, and connections 8, 9 provided on front and rear ends of the midfoot portion M and interconnecting the upper plate 3 with the lower plate 4 in the vertical direction.