The mechanical stability of a Aux-line lattice (FLL) having parameters appropriate for the high-T, superconductors is determined using the self-consistent phonon theory of lattice dynamics. Nearly parallel Aux lines (FL's) are assumed and FL pinning is neglected. The FLL becomes unstable when a phonon frequency goes to zero. At instability the rms vibrational amplitude diverges and the FL's can no longer be localized. In Bi2Sr2CaCuO&08, the instability line as a function of temperature and

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... tic field lies below but in reasonable agreement with the observed irreversibility line. In YBa2Cu307, it lies significantly below. The present instability line is a reliable upper bound to the FLL melting line. Identifying instability with melting, we find the Lindemann criterion of melting does not hold. However, the present instability lines and the melting lines obtained by Houghton et al. are found to have similar shape.