One of the main difficulties encountered in the study of existing masonry structures is found in the adequate characterization of the mechanical properties of the material. The typical features of common masonry structural members (thin bed joints, poor unitmortar bond) make it extremely difficult to obtain sufficiently large-size samples of the material components (mortar, brick or stone) and the composite allowing the application of standardized or conventional experimental tests. A possible approach to overcome this difficulty consists in the extraction and testing of small samples as a way to estimate the material properties. This paper presents an experimental programme oriented to the study of different methods for the estimation of material properties by means of unconventional tests. Since the methods analyzed cause almost null o limited damage on the existing masonry, they can be considered as minor destructive tests (MDT) usable, with some limitations, for the characterization of cultural heritage buildings. The methods investigated include penetrometer and screw pull-out tests to estimate on-site the compressive strength of mortar, the double punch tests (DPT) for the measurement in laboratory of the compressive strength of thin mortar joint samples, and laboratory tests on composite cylindrical specimens extracted from existing masonry to evaluate the masonry compressive and shear strength.