An accurate prediction of two-photon absorption (TPA) spectra, especially the position and magnitude of the peak cross-section, as well as the line width, would be of value in the design of TPA molecules for specific applications. The spectrum can be calculated using the sum-over-states (SOS) formalism, which requires accurate values for the energies of the relevant electronic states and for the transition dipole moments between these states. In addition, the form of the line-width function, such as Gaussian or Lorentzian, as well as its value, must be determined. Time-Dependent Density Functional Theory (TDDFT) has been shown to give accurate excitation energies and ground-state transition dipole moments for a wide variety of molecules. It is now possible to use this method to calculate excited-state transition dipole moments and to subsequently calculate TPA cross-sections using the SOS formalism. We report TDDFT calculations of the TPA spectra for trans-octatetraene and trans-stilbene. Gaussian functions have been used to describe the TPA line-broadening, with the width determined from experiment or previous convention. The energy levels, transition dipole moments, and TPA cross-sections calculated by this and other methods are compared to experiment and to other theoretical methods.