AbstractWe develop two algorithms for estimating member stiffnesses and masses of a structure from measured modal response in conjunction with a finite element model of the structure. The mathematical model has known geometry and topology and parameterized constitutive properties. A few of the natural frequencies are measured and the corresponding modes are sampled at certain locations in space. The proposed algorithms are based on the concept of minimizing the sum of the squares of errors, specified as an index of discrepancy between the model and the structure, over all of the measured modes. The recursive quadratic programming method is used to solve the non‐linear constrained estimation problem. Both proposed estimators can handle incompletely measured models, have robust convergence, and are amenable to modelling of complex structures. We demonstrate the use of our parameter estimation algorithm by applying it to identify the properties of a building from measured dat