Abstract: The magnetically driven capsule robot has non-contact, high penetration, and multiple control modes, and is one of the most ideal ways of diagnosing and treating gastrointestinal diseases. However, there is a risk of missing detection and retention in narrow intestines. The mathematical model and influencing factors of the friction resistance of the capsule robot in the biological intestine are the theoretical basis for the efficient driving and precise control of the capsule robot. This paper deals with the condition of capsule robots squeezing and running through curved rabbit small intestines. The nonlinear viscoelastic constitutive model is used to describe the mechanical characteristics of the intestine, and the theoretical model of the friction resistance of the capsule robot in the curved intestine is established. The mechanical parameters of the rabbit small intestine and the friction coefficient between the capsule and the intestine are obtained experimentally. The influence of geometric parameters such as the curvature of the small intestine, the length of the capsule, and the radius of the capsule on the friction resistance of the capsule are analyzed with the theoretical model. The results show that the friction resistance of the capsule robot can be equivalent to the frictional force generated by overcoming the bending moment of the intestine, plus the frictional force generated by eccentric squeezing in the straight intestine. Reducing the curvature of the intestine or increasing the radius of the capsule robot will increase the motion resistance of the capsule robot. The length of the capsule is the most sensitive factor of the capsule's friction resistance in curved intestines, and the friction resistance of the capsule will increase significantly as the length of the capsule increases. The results of this paper will provide theoretical support for the study of the resistance of capsule robots moving in the human gastrointestinal tract and experimental modelling. The research findings will also serve as a reference for the driving and precise control of magnetically-driven capsule robots.