The invention relates to equipment for drilling a vertical borehole in hard ground, the equipment comprising:

• casing put successively into place in the borehole;
• a drilling machine having a rotary cutting head and presenting a structural frame;
• torque and thrust transmission means having a first end secured to the structural frame of the drilling machine; and
• securing means for securing the second end of the torque and thrust transmission means in translation and in rotation to said casing.