*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.*