Small, fibre-based endoscopes have already improved our ability to image deep within the human body. A novel approach introduced recently utilised disordered light within a standard multimode optical fibre for lensless imaging. Importantly, this approach brought very significant reduction of the instruments footprint to dimensions below 100 μm. The most important limitations of this exciting technology is the lack of bending flexibility - imaging is only possible as long as the fibre remains stationary. The only route to allow flexibility of such endoscopes is in trading-in all the knowledge about the optical system we have, particularly the cylindrical symmetry of refractive index distribution. In perfect straight step-index cylindrical waveguides we can find optical modes that do not change their spatial distribution as they propagate through. In this paper we present a theoretical background that provides description of such modes in more realistic model of real-life step-index multimode fibre taking into account common deviations in distribution of the refractive index from its ideal step-index profile. Separately, we discuss how to include the influence of fibre bending.