A formula for the necessary hull girder bending stiffness required to avoid serious springing vibrations is derived. The expression takes into account the zero crossing period of the waves, the ship speed and main dimensions. For whipping vibrations the probability of exceedance for the combined wave- and whipping induced bending moment is derived under the assumption that the maximum peak value in a whipping sequence occurs simultaneously with a peak in sagging wave-induced bending moment, but that the magnitudes of these two peaks are statistically independent. The expression can be written as the usual Rayleigh distribution for the wave response multiplied by a factor independent of the significant wave height. Finally, the springing and whipping predictions are compared with model test results.