A push/pull operating device includes first and second operational devices mounted to two sides of a door. The first operational device includes a first bracket having two slots. A fixing plate is pivotably mounted to the first bracket. Two engaging rods extend through the slots of the first bracket. The fixing plate can be pivoted to a position where through-holes in a latch device and through-holes are aligned with the engaging rods. Thus, the push/pull operating device can be used with differently handed doors and different latch devices having different through-hole locations.