The neural or mental simulation of actions is a powerful tool for allowing cognitive agents to develop that are crucial for learning and memorizing key aspects of challenging skills. In previous studies, we developed an approach based on the animation of the redundant human body schema, based on the Passive Motion Paradigm (PMP). In this paper, we show that this approach can be easily extended to hyper-redundant serpentine robots as well as to hybrid configurations where the serpentine robot is functionally integrated with a traditional skeletal infrastructure. A simulation model is analyzed in detail, showing that it incorporates spatio-temporal features discovered in the biomechanical studies of biological hydrostats, such as the elephant trunk or octopus tentacles. It is proposed that such a generative internal model could be the basis for a cognitive architecture appropriate for serpentine robots, independent of the underlying design and control technologies. Although robotic hydrostats have received a lot of attention in recent decades, the great majority of research activities have been focused on the actuation/sensorial/material technologies that can support the design of hyper-redundant soft/serpentine robots, as well as the related control methodologies. The cognitive level of analysis has been limited to motion planning, without addressing synergy formation and mental time travel. This is what this paper is focused on.