Since the strings of a piano cannot radiate sound due to their small sections, the vibrations are transmitted through the bridges to the piano soundboard to increase radiation. This complex structure is made of a main spruce panel ribbed by several beams (ribs) in a direction orthogonal to the grain, and by two curved beams (bridges) in a direction nearly parallel to the grain. To understand the influence of superstructures (ribs, bridges) on the vibro-acoustic behavior of the soundboard, an analytical modeling is presented here based on a variational approach taken into account plate's and ribs' energies. The study is carried out on a simplify rectangular soundboard with special orthotropy and a single straight bridge. Bending, torsion and offset of the ribs are taken into account. In order to calculate the eigenmodes of the ribbed orthotropic plate, the whole vibratory problem is decomposed on the basis of simply supported unribbed plate modes. Examples of modal shapes of the soundboard and images of the plate's velocity field in response of a driving force applied to the bridge are given. The influence of the bridge and the localization phenomenon above roughly 1kHz will be discussed. This analytical methodology appears as an alternative for the finite element modeling and is particularly adapted for a parametrical study. The numerical tool developed can be used by piano manufacturers to predict the influence of the numbers/geometry of ribs and bridges on the sound of the instrument.