A method for the stabilization of slopes and/or terrain which are unstable or subject to landslides, by inserting drainage devices. A vertical shaft with a concrete lining or a microtunnel (1) is constructed and an automatic drilling unit (8) is position therein. The drilling unit has at least one drilling head (6), a magazine of rods (11), and robotic devices able to pick up the rods (12) from the magazine and take them to the drilling head, the rods (12) being constituted by the drainage pipes (5); the head is controlled to perform drilling operations, with simultaneous laying of the drainage pipe. The drainage pipes are constituted by a tubular steel element, whose walls contain holes which house a microfiltration valve filled with water-soluble material to prevent the passages from becoming obstructed during drilling; when the pipe has been laid, the water-soluble material dissolves, thus cleaning the passages.