In this paper we introduce a body-compliant Modular Snake Robot executing rolling gaits on different cylindrical geometries. In the state of the art it is considered that an active shape adaptation to the terrain while a gait is executed produces better performances than a simple pre-programmed stiff motion without feedback. Several attempts to reproduce such behaviors in snake robots range from compliant shape controllers (acting in joint space) to torque control strategies of elastic actuated joints. In our proposal, we incorporate compliant elements in a modular snake robot structure to passively adapt the robot’s shape to the environment. The gait control remains simple by acting directly in the robot’s joint space with known gait generation schemes. To validate our results we performed experiments with compliant modular snake robots rolling on pipes with different geometry characteristics such as different diameters, smooth surfaces, surfaces with presence of obstacles (terrain bumps), and considerable changes in diameter in a single robot run. We evaluated the performance across different robot’s body-compliance values, measuring the speed of locomotion as well as the power consumption. Our results show that providing a good selection of body compliant elements is a way to maintain high locomotion performance (at least while rolling on pipes) without including additional complex control artifacts to the simple open-loop cyclic gait controller.