We propose a technique to assess the vulnerability of the power system state estimation. We aim at identifying the measurements that have a high potential of being the target of false data injection attacks. From the perspective of the adversary, such measurements have the following characteristics: ① being influential on the variable estimates; ② corrupting their measured values is likely to be undetected. Additionally, such characteristics should not change significantly with the system operation condition. The proposed technique provides a systematic way of identifying the measurements with such characteristics. We illustrate our methodology on a 4-bus system, the New England 39-bus system, and the IEEE 118-bus test system, respectively.