Dynamic stress response of the double bottom structure of a bulk carrier to wave loadings was investigated by the stochastic method. Wave-induced loads on the double bottom, as well as the hull girder vertical wave bending moment, were calculated by the new strip method for the ship motion analysis. The phase differences and the correlation coefficients between the dynamic sea pressure and the cargo inertia force were evaluated and it was found that these two loads act generally in the opposite direction. Stress response functions of the double bottom structure were obtained by the quasi-static structural analysis of a 3-dimensional model for the entire hold part. The short-term and the long-term predictions of stresses in irregular seaways were made based on the random response theory for linear systems. Special attention is given to the longitudinal stresses in the bottom shell platings for which the superposition of stresses of longitudinal and transverse strength is necessary. Correlation coefficients between the hull girder vertical wave bending stresses and the alternating double bottom bending stresses were investigated in the short-term long crested irregular seas. An approximate formula is presented for the superposition of these two kinds of stresses in terms of long-term predicted values. Based on the above results, considerations were made on the selection of the design criteria for the double bottom strength in waves.