The artificial rain (pH 4.0, pH 5.6 and pH 6.85) and weathering simulation test are applied in dolomitic marble for the prediction of deterioration of the stone monuments constructed with carbonate rock by acid rain. pH of the applied rain all increase to about neutral pH after reaction of marble. The contents of $Ca^{2+}$ and $Mg^{2+}$ have increased more than twofold in two acid rain and deionized neutral rain after reaction of marble. The weight of marble is expected to decrease $0.00037kg/m^2$ each test cycle by pH 4.0 rain. This weight reduction rate of marble is 1.4 and 3.1 times more in pH 5.6 and pH 6.85 rain respectively, and 3.7 times more in only artificial weathering test. The compressive strength of marble is expected to decrease 0.2468, 0.1791 and $0.1280kg/m^2$ per test cycle with pH 4.0, pH 5.6 and pH 6.85 rain, respectively. These results mean that more acidic rain more enfeeble the strength of marble. Dolomite and small amount of calcite are precipitated in the rains after reaction of marble.