[en] Isoscalar giant resonances of arbitrary multipolarity in deformed nuclei are studied with the help of the variational principle within the framework of the nuclear elastic vibration. A particular attention is given to the fragmentation of the giant monopole and quadrupole resonances. It is shown how the nuclear surface deformation contributes to the fragmentation through the coupling between the monopole and quadrupole modes of oscillation. Simple formulas for the giant resonance energies of deformed nuclei are obtained for both axial and non-axial deformations. Surface tension and Coulomb repulsion are included in the course of formulation but practical evaluations are made without them. Most numerical results are concerned with well-deformed nuclei such as those around A=150