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Finite-element modeling calculations reveal the origin of the remarkably large elastic strains in diamond observed in recent experiments at multimegabar pressures. This approach provides a means to determine the pressure dependence of the yield strength of strong materials used in the gasket, and allows us to examine quantities that are not accessible experimentally such as the stress and strain relations in diamond. Stress tensor elements are obtained near the tip where large modifications in the optical properties of diamond have been observed.