A rotary drilling device is disclosed of the type having a body connected to a rotary drive system for rotation about a primary axis in order to bore into the ground to form a cylindrical hole. The device has a rotary cutting member mounted on one side near the bottom of the body for rotation about an inclined axis of rotation which forms an angle with the primary axis of rotation. A counter-reaction member is disposed on the side of the body away from that carrying the cutting member and near its bottom. The counter-reaction member is constructed and positioned so as to be in contact with only the concave bottom of the hole and so that the maximum radial projection from the primary axis of rotation of any part of the counter-reaction member is less than the radius of the hole, with the highest point of the surface of contact between the counter-reaction member situated below a line defined by the intersection between the concave bottom of the hole and its cylindrical side wall. The counter-reaction member has a convex surface in contact with and closely conforming to the concave surface of the bottom of the hole.