Abstract In this work, the ground and low-lying excited states in GaAs tetrapod-shaped nanocrystals and in CdTe/CdS core/shell tetrapod-shaped nanocrystals are computed in the case of a finite confinement potential model using the finite element method and the effective mass approximation. For the single material tetrapod, electron energy levels are studied as a function of size parameters and the intensity of externally applied electric and magnetic fields, while for the core/shell tetrapod the electron and hole states are analyzed relative to size parameters of the core and shell thickness. The results show that the energies are strongly influenced by the tip-arm geometry, arm diameter, shell thickness and the intensity of the electric and magnetic fields.