A general approach to the problem of evaluating the effectiveness in a reactor of plane control sheets is described. A formal expression for the critical equation of a reactor containing plane parallel control sheets is derived under very general conditions. The expression is simplified for cases of practical interest where the sheet spacing is large compared to the smaller of L or With this limitation explicit and easily soluble, critical equations are derived for thermally black control sheets in a number of interesting arrangements. In particular, the critical equation for a rectangular parallelepiped reactor containing an arbitrary number of equally spaced control sheets placed anywhere in the reactor core is written in easily soluble form. Extension of the techniques to more complicated situations is discussed.