Historically the conformal projections have been used for mapping not only the Earth, but other celestial bodies as well. Their application enables preserving the shape of the relief features on the maps, which is extremely important for various analyses of celestial bodies’ surfaces. For many small bodies of the Solar system the International Astronomical Union recommends to apply a triaxial ellipsoid as a reference surface. But if the conformal projections for the reference surfaces of a sphere and an ellipsoid of revolution already exist, obtaining these projections for a triaxial ellipsoid will be significantly complicated, and the task of preserving the shape of relief features still actual. In general, the article deals with cylindrical and azimuthal projections of the meridian section for global mapping the celestial body surface in accordance with the idea formulated by prof. L. M. Bugaevsky. The projections are implemented for mapping of Phobos, moon of Mars.