Abstract: It is difficult to describe the deterioration mechanism and permeability evolution mechanism of rock materials by the traditional numerical method of seepage flow. A finite volume numerical method is proposed for the weakening strength of rock mass induced by seepage water absorption. The seepage process of water and the deformation and destruction process of rock mass are solved with the finite volume method by using the Gauss divergence theorem, and a theoretical model for modulus and strength of the weakening rock mass induced by the matrix suction is established and the corresponding mathematical expressions are given. Based on the isotropic pore seepage model considering a water weakening algorithm, the softening process of a powder sandstone sample and the uniaxial compression process of specimens with different water absorption time are simulated under both low and high boundary fluid pressures. The numerical examples show that the higher the pressure of boundary fluid, the faster the sample reaches the overall saturation state. In the early stage of seepage, the free water flow fills the pores, while it is dominated by the transformation from the free water in the pore to the matrix suction in the later stage. The boundary fluid pressure has obvious control effect on the flow rate, but has no effect on the water absorption speed of the matrix suction. With the increase of the absorption time, the strength (cohesion and internal friction angle) of the sample is gradually reduced to the residual value, and the matrix water absorption content obtained by using this method is basically consistent with the theoretical solution. This demonstrates the calculation precision of the numerical algorithm and that it can be used to analyze the seepage and stress coupling effect on actual rock mass engineering problems such as tunnel water breakthrough and surrounding rock stability.