<p>The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with a delay term in the internal feedback. The class in question consists of two strongly coupled wave equations featuring delayed and non-delayed damping terms on the first wave equation. Through a standard change of variables and semigroup theory, we address the well-posedness of the considered coupled system. Thereon, based on some observability inequalities, we derive sufficient conditions guaranteeing the exponential decay of a suitable energy. On the other hand, from the numerical point of view, we validate the theoretical results in one-dimensional domains based on a suitable numerical approximation obtained through the Finite Difference Method. More precisely, we construct a discrete numerical scheme, which in addition to being converging and conditionally stable, preserves the energy decay property of its continuous counterpart. The theoretical analysis and the implementation of our developed numerical scheme assert the effect of the time-delayed damping on the exponential stability of strongly coupled wave equations.</p>