Based on the inclusion theory, the calculation formula of additional water pressure caused by the change of external stress state of fracture water in rock mass is deduced, and its rationality and correctness are verified by numerical experiments. Then, using the rock fracture process analysis system RFPA2D-flow and considering the influence of additional water pressure, the failure process of rock mass with multiple (2, 3, and 4 fractures) parallel fractures (dip angles of 0°, 30°, 45°, 60°, and 90°) under the coupling action of stress and seepage is numerically simulated, and the conclusions are as follows: (1) When the number of fractures is small (2 and 3 fractures), for fractured rock mass with fracture dip angles of 30°, 45°, and 60°, fracture failure finally occurs along its internal fractures. Each fracture is independent of each other, and the wing fractures formed are also parallel to each other. When the fracture dip angle is 0°, the additional water pressure has the least effect on the fracture strength of fractured rock mass, and finally the overall shear failure occurs. When the fracture dip angle is 90°, the additional water pressure has the greatest influence on the fracture strength of rock mass, and the specimen finally forms tension and shear failure. For the peak strength, the rock mass with 0° and 90° fractures is significantly higher than that with 30°, 45°, and 60° fractures, and the rock mass with 45° fracture dip angle is the lowest. In addition, with the same dip angle, the rock mass strength decreases slightly with the increase of the number of fractures. (2) When there are a large number of fractures (4 fractures), for fractured rock mass with fracture dip angles of 30°, 45°, and 60°, due to the reduction of fracture spacing, the strength of rock bridge decreases, and each fracture connects with each other, resulting in fracture failure. When the fracture dip angle is 0° and 90°, the whole shear failure of fractured rock mass occurs. With the increase of the number of fractures, the damage degree of rock mass gradually increases, the range is larger and larger, and the strength decreases rapidly. (3) When the fracture dip angle is the same, the additional water pressure in the fracture decreases gradually with the increase of the number of fractures in the rock mass.