The present invention relates to an apparatus and a method for investigating surface properties of different materials, which make it possible to carry out atomic force microscopy with a simplified and faster shear force method. The apparatus according to the invention is characterized by perpendicular orientation of the measuring tip of a self-actuated cantilever with respect to the surface of the sample. A piezoresistive sensor and a bimorph actuator are preferably DC-isolated. The measuring tip is in the form of a carbon nanotube, in particular. A plurality of cantilevers can be arranged in the form of a cantilever array which is characterized by a comb-like arrangement of individual pre-bent cantilevers. The method according to the invention is distinguished by a fast feedback signal on account of the distance between the measuring tip and the surface to be investigated being regulated using the change in a DC signal which supplies the actuator.