In this paper an autoregressive model is proposed for the form and movement of a fish school swimming in a circular water tank. The form of the fish school is assumed to be an ellipse. The major and minor axes of the ellipse and the displacement angle of the school centre are used as the variables for the model. Using the observation data from a water tank experiment, the model parameters are estimated. The very low frequency components of the data are removed by using a smooth integrated random walk model. The validity of the model obtained is examined by a whiteness test of the residual.