In this paper the theoretical analysis and the results of testing of a piezoelectric cantilever for the investigation of material surfaces are presented. The cantilever consists of a thin piezoelectric plate bonded with a thin metal (e.g., molybdenum) foil. The analytical formulae for spring constants and sensitivity of such monomorph have been established. The performed analysis permits us to state the optimal parameters of the sensor dimensions and the Young's modulus of applied materials. An important factor is the position of the nodal plane and its influence on sensor sensitivity. Various combinations of ceramic plates and metal foils were theoretically analyzed, then applied in practical realizations of the sensors. The sensor with a tip was applied to a contact ultrasonic microscope, and replaced the optical sensor commonly used to measure the deflection amplitude of the tip during scanning the surfaces of the sample. Such a method enables us to create the three-dimensional images of the surface. The sensors produced were calibrated using the quasi-static method. Sensors of this kind may fulfil requirements necessary in investigating surface properties of materials applied in modern electronics and technology.