In this work the variation of the elastic properties of some marbles are presented as a function of their mineralogical composition, microstructure, density and porosity. We selected three common Italian marbles, extensively used in monuments and historical and modern buildings: the Carrara (sample from Lorano quarry), Candoglia (samples from Cava Madre and Cava Cornovo) and Crevoladossola marbles (Palissandro and Bardiglio commercial varieties). The Carrara and Candoglia are calcite marbles, whereas the Crevoladossola is a dolomitic marble containing also a small amount of phlogopite. For each marble, three orthogonal cores were cut parallel or normal to the main structural elements (i.e. foliation and lineation). From the cores we measured the bulk and grain density (using dimensions and a gas pycnometer respectively) and we calculated the interconnected porosity. Both static and dynamic elastic parameters were measured. For the dynamic parameters we measured the velocity of ultrasonic waves (vP) at room temperature and at increasing confining pressure (up to 280 MPa). The closure of microcracks at increasing pressure causes an abrupt increment of the vP. At higher pressures the relation velocity vs. confining pressure becomes linear, and reflects the intrinsic rock properties. In the Candoglia marbles microcracks close at 40 MPa, in the Carrara marble at 60 MPa and in the Crevoladossola marbles at 100-120 MPa. P-wave velocity varies with respect to the direction of propagation, and the slowest direction is always normal to the foliation plane. The Candoglia Cava Madre and Crevoladossola Bardiglio marbles display an orthorhombric seismic symmetry, whereas the Candoglia Cava Cornovo and Crevoladossola Palissandro marbles show a transverse isotropic behaviour with infinite symmetry axis normal to the foliation. The Carrara marble is almost isotropic (about 1.5%), whilst the Candoglia Cornovo marble shows the highest anisotropy (about 15%). The static elastic parameters were measured under hydrostatic conditions (during the wavespeed measurements), using strain gauges, glued on each core longitudinally and radially. In agreement with the dynamic parameters, the largest variation with confining pressure was observed at low pressure. This is particularly evident for the Crevoladossola marbles, because of their higher porosity. In all the cores normal to the foliation the maximum deformation was along the axial direction and the minimum deformation in the radial direction. The opposite applied for the other cores. Therefore the cores in which we observed the maximum vP variation with pressure are the one showing the maximum cariation in elongation.