We propose an alternative approach to treat problems with axial or spherical symmetry. Its main characteristic consists of using Cartesian coordinates instead of curvilinear coordinates as usual. To this end, we derive general mathematical expressions giving the spatial derivatives of tensors of arbitrary order along the direction normal to an arbitrary meridian plane for systems with axial symmetry, or along two orthogonal directions normal to an arbitrary radius for systems with spherical symmetry. These relations allow the reduction of the initial three-dimensional problem to a domain with a lower dimension (two for axial symmetry, one for spherical symmetry), while keeping Cartesian coordinates within this domain. The method is illustrated for the flow of a Newtonian fluid between two coaxial cylinders (Couette cell), the Weissenberg effect for viscoelastic fluids and the flow of complex fluids like liquid crystals.