In this talk, I present a canonical decomposition of operator-valued strong L^2-functions by the aid of the Beurling-Lax-Halmos Theorem which characterizes the shift-invariant subspaces of vector-valued Hardy space. I also introduce a notion of the "Beurling degree" for inner functions by employing a canonical decomposition of strong L^2-functions induced by the given inner functions. Eventually, we establish a deep connection between the Beurling degree of the given inner function and the spectral multiplicity of the model operator on the corresponding model space.