Replicating animal movements with robots provides powerful research tools because key parameters can be manipulated at will. Facing the lack of standard methods and the high complexity of biological systems, an incremental bioinspired approach is required. We followed this method to design a snake robot capable of reproducing the natural swimming gait of snakes, i.e., the lateral undulations of the whole body. Our goal was to shift away from the classical broken line design of poly-articulated snake robots to mimic the far more complex fluid movements of snakes. First, we examined the musculoskeletal systems of different snake species to extract key information, such as the flexibility or stiffness of the body. Second, we gathered the swimming kinematics of living snakes. Third, we developed a toolbox to implement the data that are relevant to technical solutions. We eventually built a prototype of an artificial body (not yet fitted with motors) that successfully reproduced the natural fluid lateral undulations of snakes when they swim. This basis is an essential step for designing realistic autonomous snake robots.