The model operators S(u) have played an important role in developing both func- tion and operator theory over the past century. In particular, the lattice of invariant subspaces and the spectrum of S(u) have been very well understood. This success led people to study the Hardy space over the bidisk. We are interested in the independent behavior of compressed shift operator S; on the Hardy space over the bidisk. In this

talk, we study the geometric structure of S, on the Buerling type quotient modules.