A wire pressing method and apparatus for a pressure terminal using a pressing punch to connect a wire to pressing blades of the pressure terminal. The pressing punch has a pressing section for press-fitting the wire and is vertically movable. A pair of walls extending in a pressing direction are arranged on both sides of the pressing section, and the pressing blades of the pressure terminal are located between the walls at the time of a pressing operation. In this manner the wire is press-fitted into the pressing blades by the pressing section while both the walls are prevented by the pressing blades from expanding outwardly. The wire pressing method and apparatus can also be used to connect a wire to pressing blades of the pressure terminal when the terminal is received in a connector housing. This is done by retaining the side walls of the terminal receiving chamber such that the side walls will not expand outwardly during the pressing operation.