This paper discusses a method to determine the elastic constants of solid materials from the measured velocities of leaky surface acoustic waves (SAWs), and it explores the feasibility of determining the mass density from attenuation data. For an anisotropic solid such as a cubic crystal, the direction-dependent velocity of a leaky SAW has been measured by line-focus acoustic microscopy (LFAM) for various propagation-directions. A set of elastic constants has then been determined by inverting the velocity data. For an isotropic solid, the elastic moduli have been determined from the leaky Rayleigh wave velocity measured by LFAM and a longitudinal wave velocity measured by a pulse-echo transit-time technique. In addition to determining the elastic constants, it has been attempted to use the leaky SAW attenuation data measured by LFAM to determine the mass density.