  A rectangular plate modeling the deck of a suspension bridge is considered.
The plate may widely oscillate, which suggests to consider models from
nonlinear elasticity. The von K\'arm\'an plate model is studied, complemented
with the action of the hangers and with suitable boundary conditions describing
the behavior of the deck. The oscillating modes are determined in full detail.
Existence and multiplicity of static equilibria are then obtained under
different assumptions on the strength of the buckling load.
