Apparatus for removing a sealing plug from a bore, the sealing plug has an outer sleeve and an inner stem retained within the outer sleeve, the removal taking place after a suitable hole has been drilled part-way into the stem, the removal apparatus has a tapered punch for forcible insertion into the hole in the stem to create an interference fit between the punch and the stem and thereafter driving the stem out of the sleeve while also retaining the stem on the punch by virtue of the interference fit, and sleeve-engaging portion engagable with the sleeve after the punch has removed the stem from the sleeve, the sleeve-engaging portion and the punch being thereafter removable from the bore to remove both the sleeve and the stem from the bore while the sleeve and the stem are both retained on the appropriate parts of the apparatus.