The optical properties of crystalline semiconductor nanoparticles with ellipsoidal shape are investigated and discussed as a function of the shape-anisotropy parameter. The optical transition-matrix elements are calculated in the dipole approximation using perturbation theory and with a direct diagonalization of the appropriate Hamiltonian. The matrix elements involving the ground and first excited states are monotonic functions of the shape-anisotropy parameter, whereas matrix elements involving the highly excited states have zeros and extrema that are reflected in the behaviour of the corresponding transition probabilities. Moreover, some matrix elements involving the excited states have discontinuity. We demonstrate that, nanoparticles with ellipsoidal shape can be grown with the infrared as well as ultraviolet features.