In the assembly process of many products a part is forced into another one. In general, the designer aims to minimise the insertion force, and maximise the extraction force or break a tamper seal to guarantee the desired irreversibility of the process. The simulations are typically very challenging because of the associated nonlinearities, arising from the (frictional) sliding contact, and from the large strains and inelastic material behaviour, possibly with damage up to failure. Moreover, although the processes are essentially quasi-static (i.e., inertial forces are negligible), the residual stresses affecting the extraction scenario vary in time driven by rheological material behaviours, especially in polymers. Three case studies are described in the communication. First, the insertion of plastic and metal trim fasteners for vehicle interiors in the automotive industry. Second, the insertion and extraction processes of non-refillable closures for spirits. Third, the assembly and opening processes of a cap, tamper seal and leak seal on a biomedical screw flask. Besides, related contact features of choice as interference, and fluid pressure penetration to assess leakage, are also discussed. In most cases, purely static implicit simulations are possible, but explicit simulations (quasi-static with mass scaling to reduce the computational cost) are typically preferred because they provide a more robust environment for comparing different designs. The simulations help to interpret the experimental results, identify and understand the main parameters affecting the product performance, and optimise the design.