Data-based methods have gained increasing importance in engineering. Success stories are prevalent in areas such as data-driven modeling, control, and automation, as well as surrogate modeling for accelerated simulation. Beyond engineering, generative and large-language models are increasingly helping with tasks that, previously, were solely associated with creative human processes. Thus, it seems timely to seek artificial-intelligence-support for engineering design tasks to automate, help with, or accelerate purpose-built designs of engineering systems for instance in mechanics and dynamics, where design so far requires a lot of specialized knowledge. Compared with established, predominantly first-principles-based methods, the datasets used for training, validation, and test become an almost inherent part of the overall methodology. Thus, data publishing becomes just as important in (data-driven) engineering science as appropriate descriptions of conventional methodology in publications in the past. However, in mechanics and dynamics, quite widely, still traditional publishing practices are prevalent that largely do not yet take into account the rising role of data as much as that may already be the case in pure data-scientific research. This article analyzes the value and challenges of data publishing in mechanics and dynamics, in particular regarding engineering design tasks, showing that the latter raise also challenges and considerations not typical in fields where data-driven methods have been booming originally. Researchers currently find barely any guidance to overcome these challenges. Thus, ways to deal with these challenges are discussed and a set of examples from across different design problems shows how data publishing can be put into practice.