This paper is built upon the deformation-assisted joining of sheets to tubes, away from the tube ends, by means of a new process developed by the authors. The process is based on mechanical joining by means of form-fit joints that are obtained by annular squeezing (compression) of the sheet surfaces adjacent to the tubes. The concept is different from the fixing of sheets to tubes by applying direct loading on the tubes, as is currently done in existing deformation-assisted joining solutions. The process is carried out at room temperature and its development is a contribution towards ecological and sustainable manufacturing practices due to savings in material and energy consumption and to easier end-of-life disassembly and recycling when compared to alternative processes based on fastening, riveting, welding and adhesive bonding. The paper is focused on the main process parameters and special emphasis is put on sheet thickness, squeezing depth, and cross-section recess length of the punches. The presentation is supported by experimentation and finite element modelling, and results show that appropriate process parameters should ensure a compromise between the geometry of the mechanical interlocking and the pull-out strength of the new sheet–tube connections.