A novel sensor failure detection method is developed in this paper. Sensor failure considered in this paper can be any type of measurement error that is different from the true structural response. The sensors are divided into two groups; sensors that correctly measure the structural responses are termed "reference sensors" and sensors that may fail to correctly measure the structural responses are termed "uncertain sensors" henceforth. A sensor error function is formulated to detect the instants of failure of the corresponding uncertain sensor, using the measurements from reference sensors and the uncertain sensor examined. The sensor error function is derived using indirect and direct approaches. In the indirect approach, the error function is obtained from the state space model in combination with the inverse model and interaction matrix formulation. The input term is eliminated from the error function by applying the inverse model and the interaction matrix is applied to eliminate the state and all unexamined uncertain sensors except for the one examined from the error function. The direct approach uses the singular value decomposition method to establish the coefficients of the error function from the healthy measured data. The sensor failure detection formulation is investigated numerically using a four degree-of-freedom spring-mass-damper system and experimentally using a 4-m-long NASA eight-bay truss structure. It is shown by means of numerical and experimental results that the sensor failure formulation developed correctly detects and isolates the instants of sensor failure and can be implemented in real structural systems for sensor failure detection.