Various approaches and structures emerged recently to design continuum robots. One of the most promising designs regards a new concept of continuum concentric push-pull robots (CPPRs) that have the characteristic of combining several key advantages of tendon actuated, multi-backbone, and concentric tube ones (direct curvature actuation, small outer/inner diameter ratio, free lumen, etc.). Geometrically-exact models of such recently introduced robots are yet to be developed to gain leverage of their full potential. This article extends beyond usual definitions of Cosserat rod theory in order to take into account this new type of continuum robots, constituted by sliding rods, in a shape of tubes whose cross-sections are neither uniform nor symmetrical along their entire length. The introduced model is capable of considering versatile design options, external loads, 3D deformations, an arbitrary number of tubes and profiles of the centroid lines, as well as a new actuation method consisting of an input rotation. Numerical simulations and experiments on CPPR prototypes validate our model.