Relativistic Elasticity in Minkowski flat spacetime, or more generally in Lorentzian manifolds, has been the subject of recent studies in mathematical physics, as well as in physics (e.g. studies by Kolev, Desmorat and Hudelist). During the talk we define the Minkowski flat spacetime, as well as, some of its generalisations. Furthermore, we will introduce the concept of relativistic elasticity and formulate some of the associated results. Lastly, we will reformulate some of the related tensors into the language of matrices.