A new method is proposed for the identification of stiffness parameters for linear elastic structures subjected to static loads. The structural stiffnesses are identified at the element level utilizing forces and displacements measured on a subset of the degrees of freedom used to define the structural model. This method is capable of determining major changes in structural properties at the element level, including element failure.The effect of errors in force and displacement measurements are investigated utilizing a Monte Carlo analysis. This stochastic simulation may be performed prior to the actual test in order to establish an acceptable error limit for instrumentation. Also, this procedure provides important information regarding the best degrees of freedom to measure in order to identify a specific subset of the structural parameters.The scheme is suited for problems where the number of linearly independent measurements is less than the number of unknown structural parameters. Examples are presented which demonstrate the method.