This paper presents a distributed method for quantifying and evaluating static voltage stability of radial distribution networks. Firstly, based on the Distflow power flow equation, a power flow equation system with the slack node is established, and the Jacobian matrix corresponding to the state variables is obtained. The Jacobian matrix is reduced by matrix transformation, and the determinant of the reduced Jacobian matrix can be used as an evaluation index of the voltage stability of the distribution network. It is found that the reduced Jacobian matrix belongs to diagonally dominant matrix. The diagonal elements corresponding to each node of the distribution network can be used to evaluate the voltage stability, and then an approximate voltage stability evaluation index can be obtained. In addition, diagonal elements can be computed distributed by the node in which they are located. The feasibility and effectiveness of the proposed method are verified in the IEEE33-bus distribution network system.