These Proceedings of the 5th International Conference "Computational Mechanics and Virtual Engineering" COMAT 2013 include 58 papers, which analyze many important practical applications. The topics range from numerical simulations regarding the determination of stresses in all plies of various composite laminates, structural synthesis for redundant industrial robots with more than 6 axes, and the sound attenuation in a sonic composite with point defects studied using a new method that combines the features of the cnoidal method and the genetic algorithm, to a set of dual vectors based methods for rigid body displacement and motion parameterization, vibrations of heterogeneous curved beams subjected to a radial force at the crown point, and computation of the longitudinal tensile break stress of multiphase composite materials with short fibers as reinforcement.