Magneto-electric coupling phenomena in EuTiO3 are of considerable fundamental interest and are also understood to be key to reported multiferroic behavior in strained films, which exhibit distinctly different properties to the bulk. Here the magneto-elastic coupling of EuTiO3 is investigated by resonant ultrasound spectroscopy with in-situ applied magnetic field and stress as a function of temperature ranging from temperatures above the structural transition temperature, Ts, to below the antiferromagnetic ordering temperature Tn. One single crystal and two polycrystalline samples are investigated and compared to each other. Both paramagnetic and diamagnetic transducer carriers are used, allowing an examination of the effect of both stress and magnetic field on the behaviour of the sample. The properties are reported in constant field/variable temperature and in constant temperature/variable field mode where substantial differences between both data sets are observed. In addition, elastic and magnetic poling at high fields and stresses at low temperature has been performed in order to trace the history dependence of the elastic constants. Four different temperature regions are identified, characterized by unusual elastic responses. The low temperature phase diagram has been explored and found to exhibit rich complexity. The data evidence a considerable relaxation of elastic constants at high temperatures, but with little effect from magnetic field alone above 20 K, in addition to the known low temperature coupling.