An instability can potentially operate in highly irradiated disks where the disk sharply transitions from being radially transparent to opaque (the "transition region"). Such conditions may exist at the inner edges of transitional disks around T Tauri stars and accretion disks around active galactic nuclei. We derive the criterion for this instability, which we term the "irradiation instability," or IRI. We also present the linear growth rate as a function of β, the ratio between radiation force and gravity, and c s, the sound speed of the disk, obtained using two methods: a semi-analytic analysis of the linearized equations and a numerical simulation using the GPU-accelerated hydrodynamical code PEnGUIn. In particular, we find that IRI occurs at β ~ 0.1 if the transition region extends as wide as ~0.05r, and at higher β values if it is wider. This threshold value applies to c s ranging from 3% of the Keplerian orbital speed to 5%, and becomes higher if c s is lower. Furthermore, in the nonlinear evolution of the instability, disks with a large β and small c s exhibit "clumping," extreme local surface density enhancements that can reach over 10 times the initial disk surface density.
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