Variational and boundary integral equation techniques are two of the most useful methods for solving time-dependent problems described by systems of equations of the form 2 ? u = Au, 2 ?t 2 where u = u(x,t) is a vector-valued function, x is a point in a domain in R or 3 R, and A is a linear elliptic differential operator. To facilitate a better und- standing of these two types of methods, below we propose to illustrate their mechanisms in action on a specific mathematical model rather than in a more impersonal abstract setting. For this purpose, we have chosen the hyperbolic system of partial differential equations governing the non stationary bending of elastic plates with transverse shear deformation. The reason for our choice is twofold. On the one hand, in a certain sense this is a hybrid system, c- sistingofthreeequationsforthreeunknownfunctionsinonlytwoindependent variables, which makes it more unusual and thereby more interesting to the analyst than other systems arising in solid mechanics.