The flexible robot is widely used in a variety of fields such as medical treatment, rescue and disaster relief, industry, and agriculture. Using elastic materials to prepare flexible robot body structures is the core of the study of flexible robots. Due to the small selection of materials, single preparation method, and long fabrication time, in this study, a new method of gas-assisted extrusion (GAE) of elastic material round-tube for flexible robot body was proposed, and the numerical simulation of GAE was carried out with nonsilicone elastic material round-tube under different viscosities. The results showed that with the change of viscosity, the velocity, pressure drop, and shear rate of melt in all directions change accordingly. When the viscosity is too small or too large, it is easy to bring negative effects on the GAE process of elastic materials. TPE and TPU were completely plasticized in the GAE, and the surface of the extruded elastic products was smooth and straight, with full gloss. Therefore, in the preparation of the flexible robot body, nonsilicone elastic materials and GAE forming methods can be considered.