The connector includes an inner contact formed of a plate member inserted into a recess of a plug contact, the plate member having a first constituent portion including an elastically displaceable contact portion and a second constituent portion including a pressing portion that is elastically displaceable independently of elastic displacement of the contact portion, part of a sheet-like connection target in which a flexible conductor is exposed on at least one surface being sandwiched between the pressing portion and an inner surface of the recess in a direction orthogonal to the fitting axis, the inner surface of the recess coming into contact with a front surface of the connection target while the pressing portion coming into contact with a back surface of the connection target.