Sole structure for shoes and shoe with the sole structure

Disclosed is a sole structure for shoes, which includes a lower midsole. The lower midsole includes a medial-side midsole portion which extends in a medial side portion of a heel region supporting a heel of a wearer's foot, and a lateral-side midsole portion which extends in a lateral side portion of the heel region, and which faces, and is spaced apart from, the medial-side midsole portion in a foot width direction. The lateral-side midsole portion includes supports which are arranged adjacent to each other in a longitudinal direction with a gap interposed therebetween and which support the wearer's heel, and a coupling portion which is provided in the gap, and couples the adjacent supports to each other to reduce displacement or twist in the foot width direction occurring between the adjacent supports.