This book collects the latest advances and innovations in the field of applied mathematics and computational mechanics, as presented at the 2nd Workshop GIMC SIMAI YOUNG, held in Naples, Italy, on July 10–12, 2024. The workshop was the joint effort of Computational Mechanics Group of the Italian Association of Theoretical and Applied Mechanics -AIMETA (GIMC) and  Italian Society of Applied and Industrial Mathematics (SIMAI) and was meant to highlight the works of young researchers in the field. Topics include mathematical models for socio-epidemiological dynamics, efficient numerical methods for evolutionary PDEs, multi-scale approaches and machine learning techniques in material modelling, nonlinear material behaviour, computational methods for shells and spatial structures, assessment, monitoring, and design of masonry structures, particles in numerical simulations, non-Newtonian complex fluids, mathematical modelling in mechanobiology and oncology, mechanics of biological systems and bioinspired materials, computational approaches for complex dynamical systems, optimization methods for classical and data-driven approaches. The contributions, which were selected by means of a rigorous peer-review process, present a wealth of exciting ideas that will open novel research directions and foster multidisciplinary collaboration.