This work is an attempt to the dynamic identification of base isolation systems from earthquake response records. A very simple base isolation system is considered, composed of only four lead rubber bearings at the four corners of a building in the city of Kushiro in northern Japan. The acceleration of the building, recorded during the 2003 Tokachi-oki earthquake, is used for the identification. The identification procedure is based on the minimization of the distance between the acceleration of the building measured during the earthquake and the simulated one obtained by using a model presented at CUEE-12. A state-of-the art optimization algorithm (CMA-ES), based on the adaptation of the covariance matrix of a multivariate Gaussian probability distribution, is used to guide the identification process. The model parameters, obtained by identification from three laboratory tests performed in 1996 and in 2004, are used as a reference for the definition of the search space where the system parameters are expected to be. The optimal solution is given in probabilistic terms, namely the average value, standard deviation and coefficient of variation of the system parameters. The work is completed with a critical analysis of the minimal system response required to obtain a realistic prediction of the system parameters for the model considered.