Abstract: A method is proposed to detect damages and assess the status of an existing structure from static test data. The real structure is represented by finite element model that is described by the member constitutive parameters and kernel matrix. Two algorithms by Gauss-Newton method for identifying those parameters based on two kinds of error definition under incomplete measurement are developed. Using Monte Carlo method, the effectiveness and stability of two algorithms are investigated when measurement errors exist. The first algorithm is distinguished in that the sensitivity matrix is not affected by the measurement error of displacements. The identified constitutive parameters are at the element level, and a statistical approach by a hypothesis test is introduced to locate and assess the damages of elements. Numerically examples are presented to demonstrate the validity and accuracy of the damage assessment algorithm.