This book is based on my master's research in Institute of Electro-Optical Engineering in National Chiao Tung University, 2005. It's entitled "Analysis of Defect Modes of Two-Dimensional Photonic Crystal Nano-Cavities". In this study we demonstrate some principles and techniques for the simulation of two-dimensional photonic crystals and photonic crystal nano-cavities formed by defects in two-dimensional photonic crystal slabs. Photonic band structures within and without a defect were simulated using both 2D and 3D plane wave expansion method and finite difference time domain method. Then a basic symmetry analysis was carried out by the group theory. Resonant frequencies, mode profiles, and quality factors of photonic crystal micro-cavities in finite height dielectric slabs were calculated by three-dimensional finite difference time domain method.