The bead model is a random point field on Z × R which can be viewed as a scaling limit of dimer model on a hexagon lattice. We formulate and prove a variational principle similar to that of the dimer model, which states that in the scaling limit, the normalized height function of a uniformly chosen random bead configuration lies in an arbitrarily small neighborhood of a surface h_0 that maximizes some functional which we call as entropy. We also prove that the limit shape h_0 is a scaling limit of the limit shapes of a properly chosen sequence of dimer models. There is a map from bead configurations to standard tableaux of a (skew) Young diagram, and the map is measure preserving if both sides take uniform measures. The variational principle of the bead model yields the existence of the limit shape of a random standard Young tableau.