Abstract Analytical models of linear elastomechanical systems are often updated by model parameter estimation using input–output measurements or modal test results. The structure of the model equations and the parametrisation of the spatially discretised model—often a sum of matrices multiplied each by a dimensionless adjustment parameter—are usually assumed to be consistent with the system under test. Thus, the analytical model can be corrected by estimating the actual values of the dimensionless adjustment parameters. There is, however, a lack of measurement information that is caused by the difference between the number of degrees of freedom (dof) of the analytical model and the number of measured dof. That is not only due to large-scale models but is also due to the fact that rotational dof are generally not measured. This lack of information is also the reason for the non-linear character of this kind of model updating because it is in general a simultaneous parameter and state estimation problem. Due to its intrinsic non-linearity the inverse problem is ill-posed with the latent risk of biased parameter estimates. In this paper it is shown that the problem of updating linear analytical models can be transferred to a multiparameter eigenvalue problem that needs only a minimum set of test data for estimating the actual model parameter values with a negligibly small risk of biased estimates. The presented method is well-founded by its rigorous mathematical deduction.