The use of thermally black control sheets in a reactor is examined for three special cases: a finite slab reactor with a control sheet at its midplane, an infinite slab reactor containing an array of uniformly spaced control sheets, and a finite slab reactor with two control sheets placed symmetrically about the reactor centerline. The critical equation is obtained in each case and the physical significance of the solutions is examined by allowing the critical parameters to take limiting values. The conclusions reached are: (1) For τ/L2 « 1, thermally black control sheets are effectively black to all neutrons and divide the reactor into independent parts provided the distance W between control sheets, or core boundary and control sheet, is » τ3/2/L2. For W ≾τ3/2/L2, the control sheet is less effective. (2) For τ/L2 » 1 and W » τ/L, thermally black control sheets effectively divide the reactor into independent parts. For W ≾τ/L, the control sheets are less effective. (3) For τ/L2 » 1, W/L » 1, and W2/τ ∼ 1, a thermally black control sheet is relatively ineffective as compared with a sheet black to all neutrons. (4) The criteria for placing a given number of sheets most effectively in a reactor depend upon the worth of the sheets as determined from the conditions above. Thus, for sheets which are essentially black to all neutrons, the position of maximum effectiveness occurs when the reactor is cut into pieces of nearly equal size. However, for sheets of less worth, the positions of maximum effectiveness occur closer to the center of the reactor. In the limiting case, where the control effectiveness is very much smaller than the leakage from the reactor, the sheets should be placed about the reactor center, separated by about one diffusion length. It is pointed out that a very weak thermally black control element in a very large reactor may produce a large effect on the power distribution.