Abstarct: In many applications, researchers are interested to approximate a probability distribution function. The Edgeworth expansion is a method for this aim. The Edgeworth expansion is a series that approximates a probability distribution in terms of its cumulants. One can derive it by first expanding the probability distribution in Hermite orthogonal functions and then collecting terms in powers of the sample size. In this thesis, by using a version of Stein’s Identity and properties of Hermite polynomials, we derive an expansion for posterior distributions which possesses these features of an Edgeworth series. Then, we compare the performance of the proposed series with the previous ones from a Bayesian perspective. Finally, two examples are provided to illustrate the accuracy of the proposed expansion.