The maturation process of beef improves meat quality. Several bio-physical-chemical changes occur during ageing. Often, they emerge macroscopically as variations in the mechanical properties of the tissue. Most of the actual testing methods are destructive. Therefore, the number of tested samples is limited. Elastography was born as a medical imaging modality to estimate noninvasively the elasticity of soft tissues. Thus, its application to monitor ageing could help to overcome some drawbacks of destructive methods. However, its use is minimum in industry. In this work, we study the feasibility of using surface wave elastography (SWE) to monitor beef ageing. We tested 25 samples for 21 consecutive days. The results show a decay close to 50% in the shear elasticity of all samples. In addition, the rate of decay show that the elasticity reduction is greater in the first days for most samples. These results are consistent with previous knowledge in this area, which encourages further research to improve the method and increase its performance and reliability.