A Bayesian probabilistic approach is presented for selecting the most plausible class of models for a structural or mechanical system within some specified set of model classes, based on system response data. The crux of the approach is to rank the classes of models based on their probabilities conditional on the response data which can be calculated based on Bayes' theorem and an asymptotic expansion for the evidence for each model class. The approach provides a quantitative expression of a principle of model parsimony or of Ockham's razor which in this context can be stated as "simpler models are to be preferred over unnecessarily complicated ones." Examples are presented to illustrate the method using a single-degree-of-freedom bilinear hysteretic system, a linear two-story frame, and a ten-story shear building, all of which are subjected to seismic excitation.