Modern plant-based meat analogues should have a pronounced fibrous structure as an important characteristic. In this study, we demonstrate that the combination of high moisture extrusion cooking (HMEC) with well-defined shear during cooling is a new process to make fibrous products using common meat analogue ingredients. The shear was applied via a cooling die attached to the extruder that was specially designed for that purpose. The in–house developed cooling die consists of two sequential rotating inner cylinders with a separate drive-unit in an outer cylinder that can be thermo-regulated. Three rotational speeds of the inner cylinder, 45, 75 and 105 min−1, were tested for pea protein isolate, soy protein concentrate, vital wheat gluten and blends of pea or soy with gluten. A large effect on macro- and micro-texture and anisotropy index was found when the concentration of gluten was increased. The different ingredients and blends had different optimal conditions and reacted differently to the applied shear. Interestingly, the angle of the fibers observed in the samples differed at the different rotational speeds. This was attributed to the shear thinning behavior of the plant proteins and the velocity gradient in the rotating die, arising from the temperature and viscosity gradient. The ability to change the shear rate as an independent parameter in the rotating cooling die is unique and allows texture adjustments during processing. This is an important improvement for industrial HMEC and opens new product design possibilities.