The factor analysis model has been widely applied to study finance problems. The purpose of this paper is to introduce a Bayesian approach for analysing the factor analysis model. The advantages of the proposed Bayesian approach over the classical maximum likelihood rest on its capability to incorporate additional prior information, to determine the number of factors in an objective manner, and to produce parameter and factor score estimates with good statistical properties. Based on recently developed tools in statistical computing, such as the Gibbs sampler and path sampling, methods for obtaining the Bayesian estimates of the parameters and factor scores, and a procedure for computing the Bayes factor for selecting the appropriate number of factors in the model, are developed. The proposed new methodologies are applied to analyse a data set taken from the Hong Kong stock security market. It is found that a three-factor model with a generic market factor can be used to describe the systematic components of asset returns.