New rigorous approach to the analysis of 2-D photonic crystals is suggested in the paper. The approach is based on the method of exact absorbing conditions, which provides accurate and reliable numerical results valid for long-duration simulations and resonant waves scattering. Several problems have been solved, which demonstrate the effectiveness of the proposed approach and its potential for obtaining reliable results for theoretical and practical applications. New results were obtained concerning bandgaps and passbands of compact crystals, electromagnetic characteristics of resonant cavities and basic waveguide components in photonic crystals, energy accumulation in resonant cavities, and radiation effects caused by the backward waves in photonic crystals.