The invention relates to an improved rod pushing and pulling machine suited for use in underground pipe bursting and replacement with a rod string wherein each rod has at least one radially enlarged upset thereon. The machine includes a housing or frame having a front wall with an access opening therein through which a rod string can extend. At least one main thrust cylinder is mounted on the housing. A movable carriage connected to the thrust cylinder engages the rod, drives it in a pushing or pulling direction, and then releases it for another stroke. Between strokes, a “bungee” vise holds the rod string so that it does not slip back in the opposite direction.