This thesis systematically derives an innovative approach, called FOMFE, for fingerprint ridge orientation modeling based on 2D Fourier expansions, and explores possible applications of FOMFE to various aspects of a fingerprint identification system. Compared with existing proposals, FOMFE does not require prior knowledge of the landmark singular points (SP) at any stage of the modeling process. This salient feature makes it immune from false SP detections and robust in terms of modeling ridge topology patterns from different typological classes. The thesis provides the motivation of this work, thoroughly reviews the relevant literature, and carefully lays out the theoretical basis of the proposed modeling approach. This is followed by a detailed exposition of how FOMFE can benefit fingerprint feature analysis including ridge orientation estimation, singularity analysis, global feature characterization for a wide variety of fingerprint categories, and partial fin gerprint identification. The proposed methods are based on the insightful use of theory from areas such as Fourier analysis of nonlinear dynamic systems, analytical operators from differential calculus in vector fields, and fluid dynamics. The thesis has conducted extensive experimental evaluation of the proposed methods on benchmark data sets, and drawn conclusions about strengths and limitations of these new techniques in comparison with state-of-the-art approaches. FOMFE and the resulting model-based methods can significantly improve the computational efficiency and reliability of fingerprint identification systems, which is important for indexing and matching fingerprints at a large scale.