Vibrational intensities are calculated for the fundamental and overtone transitions of H2O up to approximately 18000 cm(-1). The intensities are determined from a dipole moment function expanded in the three internal bond coordinates. The expansion coefficients are computed ab initio at the second-order Moller-Plesset level of theory with a 6-311G** basis set. Vibrational wave functions are calculated either from a three-dimensional harmonically coupled anharmonic oscillator (HCAO) model which uses Morse oscillators to represent both the stretches and the bend of H2O, or from a variational calculation employing the best available potential energy surface and an exact kinetic energy operator. To obtain the most meaningful vibrational intensities we define dipole moment components using the Eckart embedding. Both the HCAO and the variational intensities agree quite well with the experimental results, which span eight orders of magnitude. From the calculations we predict that it may be possible to detect as yet unobserved vibrational transitions of H2O.