Measurement invariance concerns whether the constructs’ measurement properties (i.e., relations between the latent constructs of interest and their observed variables) are the same under different conditions. Without establishing evidence of measurement invariance, corresponding cross-condition comparisons are questionable. Although different systems have been developed in conducting measurement invariance tests, a few important issues shared by those systems remain unsolved. The current dissertation tries to use Bayesian Structural Equation Modeling (BSEM) to address three major imperative issues in studying measurement invariance. First, a new, reliable measure is developed to select a proper (i.e. truly invariant) reference indicator. Second, the issue of locating non-invariant parameters is addressed by using the Bayesian Credible Interval (BCI). Third, posterior distribution is employed to evaluate empirical consequences of non-invariance; specifically, the aim is to interpret non-invariance in terms of expected differences in observed scores across levels of latent trait (or expected differences in latent trait conditioning on observed test scores), and to provide relevant confidence limits. A series of simulation analyses show that the proposed method performs well under a variety of data conditions. An empirical example is also provided to demonstrate the specific procedures to implement the proposed methods in applied research. Extensions and limitations are also pointed out.