A relatively simple theoretical model for predicting the shock thickness is applied to the weak shock propagation through sea water, where the boric acid and the magnesium sulfate are the major relaxation processes. The relaxation effects increases the shock thickness by the factor of 103 compared with the thickness based on the classical absorption only. In seawater with the ambient pressure of 125 atm and 15℃ temperature, the effects of the boric acid are dominant when the peak pressure is less than 0.3 atm and 3 atm. For the shocks of peak pressure greater than 5 atm, the effects of the classical absorption theory is enough to describe the shock thickness. The effects of the ambient pressure and temperature on the shock thickness are also evaluated.