A machine for assembling boxes comprising five independent parts including two head walls, two side walls and a base with peripheral flanges that engage with grooves in a lower portion of the side walls and the head walls. Ends of the head walls have end tongues that are inserted into notches adjacent to ends of the side walls. The machine includes a central assembly station comprising a base ring inside which a stationary forming die is disposed. A base of a box to be formed is positioned on a lower face of the stationary forming die such that while the base of the box is held in position, horizontal push devices are activated which move the head walls and the side walls towards the base of the box which is locked in position against the lower face of the stationary forming die.