In the structural equation models, the maximum likelihood estimates of error variances can often turn out to be zero or negative. In order to overcome this problem, we take a Bayesian approach by specifying a prior distribution for variances of error variables. Crucial issues in this modeling procedure include the selection of hyper-parameters in the prior distribution. Choosing these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating a Bayesian structural equation model. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed modeling procedure. A real data example is also given to illustrate our procedure.