Summary: The main objective of this paper is to investigate the application of the EM algorithm for obtaining a Bayesian estimate of the factor score in a factor analysis model with polytomous data. The posterior distribution of the latent factor score given the manifest continuous or polytomous observations is derived, and then the EM algorithm is utilized to find the posterior mode estimate of the distribution. It is shown that both the \(E\)-step and the \(M\)-step of the algorithm are very simple. An expression for the covariance matrix of the posterior distribution is derived. Results of a simulation study are presented to illustrate some properties of the estimate and the EM algorithm.