Distribution of interacting particles on a sphere is historically a well known problem, however, ordering of systems with anisotropic interaction, specifically dipole and quadrupole interaction, remains unexplored. We solve orientational ordering of point dipoles on a sphere with fixed positional order with numerical minimization of energy and introduce order parameters needed for quantitative classification of different configurations. We find vortex ground states for different system sizes while excited states also show other configurations. We explore system response in external field where multiple orientational phase transitions emerge. We also perform simulations of orientational ordering of quadrupole systems and notice important differences between linear and planar quadrupoles. Results acquired in this thesis represent a starting point for further research on systems with anisotropic interaction on non-Euclidean geometries.