Conceiving robots with a variable stiffness continuum structure is a rapidly developing field of research. Swimming snakes provide an excellent bioinspiration source to design such type of robots characterized by variable compliant structures. Appropriate distribution of stiffness should permit to generate desired body shape deformations during swimming and displacements in a cramped space. We modelled the vertebrae anatomy of biological snakes and derived a simplified design. Via the control of the mechanical properties of universal joints, the bioinspired vertebrae compliance effectively mimicked the mechanical properties of biological vertebrae. We describe the method based on orthogonal compliant twist rods we used to build a whole snake robot skeleton. The flexible continuum robot, inspired from swimming snakes, was made of a series of optimized vertebrae. Each one has unique design parameters in order to obtain the stiffness distribution observed in swimming snakes. The resulting structure is a 3D printed monolithic nylon based variable stiffness optimized continuum snake robot. Experimental tests were performed to compare optimized and 3D printed vertebrae deflection angles. We successfully reproduced the variable stiffness observed in biological snakes and obtained the desired motions.