Axial splitting is the dominant failure mode of brittle solids under compression, yet its mechanical origin remains unclear. We show that clamped loading platens suppress lateral Poisson expansion, generating boundary-induced tensile stresses at the specimen interior – the compressive analog of wrinkling in stretched sheets. This mechanism provides a predictive strength law, relating axial splitting to tensile strength, geometry, and confinement pressure. This is validated against diverse materials ranging from rocks to ceramics, establishing axial splitting as a geometry-controlled elastic process rather than a stochastic flaw problem.