A terminal metal fitting has a wire connecting portion to which an electric wire is connected and an electrically contacting portion to which a mating terminal metal fitting is connected. The electrically contacting portion is formed in a hollow quadrilateral cylinder. The mating terminal metal fitting has an insertion to be inserted into the electrically contacting portion. The electrically contacting portion has a flat bottom wall, a ceiling wall facing the bottom wall, and a pair of elastic pieces 15a, 15b. The elastic pieces 15a, 15b are arranged in an insertion direction of the insertion. One end portions 16a, 16b of the respective elastic pieces 15a, 15b integrally continue from the bottom wall. The elastic pieces 15a, 15b each are formed obliquely from the one end portions 16a, 16b toward the other end portions 17a, 17b, respectively, with respect to the bottom wall from the bottom wall toward the ceiling wall. End faces 18a, 18b of the other end portions 17a, 17b of the elastic pieces 15a, 15b face the insertion direction of the insertion into the electrically contacting portion.