A connector 11 including a flexible engagement piece 25 which has a base end supported like a cantilever in a terminal accommodation chamber 17 for accommodating a terminal fitting and is thus deformable elastically, and has a free end 27 with which the terminal fitting to be inserted into the terminal accommodation chamber 17 is engaged, wherein the flexible engagement piece 25 having a beak 31 formed on the free end 27 to be engaged with the terminal fitting takes a shape of an inclined surface 29 having a height of a top portion 41 increased gradually from the free end 27 toward the base end in such a manner that a maximum shear area is obtained by a shear force of the terminal fitting.