Electromagnetic Acoustic Transducers (EMATs) allow non-contact ultrasonic measurements in order to characterize structures for a wide range of applications. Considering non-ferromagnetic metal materials, excitation of elastic waves is due to Lorentz forces that result from an applied magnetic field and induced eddy currents in a near surface region of the sample. EMAT's design is based on a magnet structure associated with a coil leading to multiple configurations, which are able to excite bulk and guided acoustic waves. In this work, we first present a self-developed EMAT system composed of multiple emission and reception channels. In a second part, we propose an original method in order to determine the elastic constants of an isotropic material. To achieve this goal, Rayleigh and shear waves are used and the advantages of this method are clearly highlighted. The results obtained are then compared with conventional measurements achieved with piezoelectric transducers.