Bayesian identification provides a framework that can handle both measurement and modeling errors. Furthermore it identifies a probability distribution function thus providing information on both variance and correlation of the identified properties. However, the procedure can be very costly computationally. In order to address the computational cost issue a Bayesian identification procedure based on response surface methodology is proposed. The procedure is illustrated on the problem of identifying orthotropic elastic constants from natural frequencies of a free composite plate. The procedure accounts for measurement noise, uncertainty in other input parameters to the vibration model (plate dimensions, density) as well as systematic error effects. The joint probability distribution of the four elastic ply constants is identified and characterized by mean value and variancecovariance matrix. We find that some properties, such as Poisson's ratio, are identified with much higher uncertainty than other and that significant correlation between the identified properties is present. The developed procedure allowed substantial reduction in computational cost. However, in spite of the cost reduction techniques, it remains at the edge of what is presently reasonable computation time.