The equipment serves to form consolidated soil columns having a non-circular cross- section, and comprises a mast (2, 8), a rotary (3) which is rotatable and translatable along an axis parallel to the mast, a series of hollow rods (4) temporarily unlockable from the ro¬ tary (3), and a device to vary the rotational rate of the rotary in one or more prefixed angu¬ lar ranges. A rotor (21) is directly secured to one of the rods of the string and operatively coupled to a device (20) generating control signals to vary the rotational speed of the rotary in response to the rotor angular position. A through clamp (10) is mounted to the rotatable mandrel of the rotary and is provided with locking members which can be activated to clamp a rod and make it integral to the rotary, and which can be deactivated to release the rod so as to allow the rotary to move relative to the rod.