Structural equation models are analysed in the presence of stochastic constraints. Based on a Bayesian perspective, a prior distribution on nuisance parameters in the unknown covariance matrix of error measurements with stochastic constraints is considered. An iterative procedure is implemented to produce the various Bayesian estimates with stochastic constraints. A simulation study is conducted to illustrate the accuracy and behaviour of this Bayesian approach. A real‐life example is provided to illustrate the theor