The spatial distribution of fingerprint minutiae is a core problem in the fingerprint individuality study, the cornerstone of the fingerprint authentication technology. Previously, the assumption in most research that minutiae distribution is random has been proved to be inaccurate and may lead to significant overestimates of fingerprint uniqueness. In this paper, we propose a stochastic model for describing and simulating fingerprint minutiae patterns. Through coupling a pair potential Markov point process with a thinned process, this model successfully depicts the complex statistical behavior of fingerprint minutiae. Parameters of this model can be determined by nonlinear minimization. Furthermore, experiment results show that the statistical properties of our proposed model dovetails nicely with real minutiae data in terms of the false fingerprint correspondence probability. Such evidences indicate that the proposed model is a more accurate foundation for minutiae based fingerprint individuality studies as well as the artificial fingerprint synthesis when compared to the model of random distribution.