Fault attacks are potent physical attacks on crypto-devices. A single fault injected during encryption can reveal the cipher's secret key. In a hardware realization of an encryption algorithm, only a tiny fraction of the gates is exploitable by such an attack. Finding these vulnerable gates has been a manual and tedious task requiring considerable expertise. In this paper, we propose SOLOMON, the first automatic fault attack vulnerability detection framework for hardware designs. Given a cipher implementation, either at RTL or gate-level, SOLOMON uses formal methods to map vulnerable regions in the cipher algorithm to specific locations in the hardware thus enabling targeted countermeasures to be deployed with much lesser overheads. We demonstrate the efficacy of the SOLOMON framework using three ciphers: AES, CLEFIA, and Simon. © 2020 EDAA.