Out-of-plane, or transverse, motions of plates is of paramount importance because, as in the case of straight beams and for the same reasons, plates are much less rigid when solicited in the out-of-plane than in the in-plane direction. Furthermore, the transverse response of a plate is sensitive to the presence of in-plane stresses, just as the bending of a straight beam is sensitive to the presence of a longitudinal stress. Modelling of the out-of-plane motions of plates is based on the so called Kirchhoff Love hypotheses which extends the simplifying assumptions used to establish the Bernoulli Euler model of straight beam bending to the two-dimensional case. Accordingly, the transverse motion can be described in terms of a single displacement field, the so called transverse displacement denoted Z. As Z depends on two coordinates ( x, y in the case of a rectangular plate), new interesting features arise in plate bending and torsion with respect to straight beam bending, both from the mathematical and physical viewpoints. The Kirchhoff Love model is found appropriate to deal with thin plates where the thickness is small compared with either the other dimensions of the plate or to the modal wavelengths of the highest modal frequency of interest. Though this book is strictly restricted to the case of thin plates and thin shells, it may be worth mentioning that the Kirchhoff Love model can be improved by accounting for rotatory inertia and out-of-plane shear deformation, in a similar manner as the Bernoulli Euler model can be improved, to...