Part of the compressive strength of a test specimen of rock or coal in the laboratory or a pillar in a mine comes from physical property strength and, in part, from the constraint provided by the loading stresses. Much confusion in pillar design comes from assigning the total strength change to geometry, as evidenced by the many pillar design equations with width to height as the primary variable. In tests by the U.S. Bureau of Mines, compressive strengths for cylindrical specimens of limestone, marble, sandstone, and coal were independent of the specimen test geometry when the end friction was removed. A conventional uniaxial compressive strength test between two steel platens is actually a uniaxial force and not a uniaxial stress test. The biaxial or triaxial state of stress for much of the test volume changes with the geometry of the test specimen. By removing the end friction supplied by the steel platens to the specimen, a more nearly uniaxial stress state independent of the specimen geometry is produced in the specimen. Pillar design is a constraint and physical property problem rather than a geometry problem. Roof and floor constraint are major factors in pillar design and strength.