Computational Structural Mechanics and Mathematics have always made a very powerful alliance, and the rapid advances in computer science have further strenghthened them in the form of novel mathematical models and the accompanying computational algorithms. However, despite the enormous progress already made, there is still room for continuous improvement. This reprint is clear proof of such progress. It namely contains 10 up-to-date articles accepted after strict reviews published in the Special Issue "Computational Mechanics and Applied Mathematics" of the MDPI Mathematics journal, covering a wide range of themes connected to this very topical subject. Therefore, it is our hope that this reprint, which mainly addresses the fundamental relationships between mechanics and mathematics and their applications, will be engaging and useful for various experts involved in any of both of these important research areas whose mutual goal is to ensure the sustainable safety of structures and other kinds of engineering objects.