In this paper we discuss a simple fully Bayesian analysis of the change point problem for the directional data in the parametric framework with circular normal distribution as the underlying distribution. We discuss the problem of detecting change in the mean direction of the circular normal distribution when the concentration parameter is unknown. Beginning with proper priors for all the unknown parameters, the sampling-importance-resampling (SIR) technique is used to obtain the posterior marginal distribution of the change point. The method is illustrated using the wind data (Weijer's et. al.(1995)). The method can be adapted to a variety of situations involving both angular and linear data and can be used with profit in the context of statistical process control in Phase I of control charting and also in Phase II in conjunction with control charts. Note: For softcopy of this paper, please contact the authors - email: arnab@iima.ac.in