A connector has terminal fittings (20) with a touching section (41) to be held in contact with a mating terminal (30) and a housing (10) formed with press-in holes (14, 14A), into which the terminal fittings (20) are pressed. The terminal fittings (20) are pressingly held in the housing (10) after the touching sections (41) pass through the press-in holes (14, 14A). A part of the inner surface of each press-in hole (14, 14A) of the housing (10) corresponding to a passage area of the touching section (41) is shaped to be gradually distanced from the passage area towards an apex (62, 62A) at a widthwise middle part (65) of the passage area. Accordingly, mutual abrasion of the touching section (41) and the inner surface of the press-in hole (14, 14A) can be avoided when the touching section (41) passes through the press-in hole (14, 14A).