The thesis studies the bulk deformation properties of the Skyrme nuclear energy densityfunctionals. Following simple arguments based on the leptodermous expansion andliquid drop model, the current research applies the nuclear density functional theory toassess the role of the surface symmetry energy in nuclei. To this end, one can validatethe commonly used functional parametrizations against the data on excitation energies ofsuperdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei.After subtracting shell effects, the results of our self-consistent calculations are consistentwith macroscopic arguments and indicate that experimental data on strongly deformedcongurations in neutron-rich nuclei are essential for optimizing future nuclear energy densityfunctionals. The resulting survey provides a useful benchmark for further theoreticalimprovements. Unlike in nuclei close to the stability valley, whose macroscopic deformabilityhangs on the balance of surface and Coulomb terms, the deformability of neutron-richnuclei strongly depends on the surface-symmetry energy; hence, its proper determinationis crucial for the stability of deformed phases of the neutron-rich matter and descriptionof fission rates for r-process nucleosynthesis. The results and consequent discussions fromthe thesis were published in Ref. [134].