  In this paper we study the Newton stratification on the reduction of Shimura
varieties of PEL type with hyperspecial level structure and the Newton
stratification on the deformation space of a Barsotti-Tate group with PEL
structure. Our main result is a formula for the dimension of Newton strata and
the description their closure in each of the two cases. Furthermore, we
calculate the dimension of some Rapoport-Zink spaces as an intermediate result.
