We consider how we can obtain balance incomplete block designs (BIBDs) from the splitting fields of some class of polynomials. The splitting field of polynomial,
p(x) is the smallest field in which p(x) splits as a product of linear factors. A
BIBD is considered as an arrangement of a finite set of elements into some subsets
subject to a specific defining relations. BIBDs came into existence through the
work of Authors such as R. A Fisher and F. Yates on the question of the design of
field experiments in agriculture in the 1930s. We construct BIBDs from the splitting fields of polynomials.