To analyze the foundation stability of the circular soil cave with double holes, the complex stress function is obtained for a single hole by the Cauchy integral method. The stress of any point in the soil layer under bipolar coordinates is derived based on the Schwarz alternating method by two iterations. The maximum and minimum stresses of the soil are obtained by stress coordinate transformation and the Mohr-Coulomb strength criterion is used to determine the stability state of the most dangerous point of the soil cave. The calculated results in this paper are compared with the exact analytical solutions and the ABAQUS numerical simulation results. Application to an engineering example proves that the Schwarz alternating method has higher precision. The stability coefficient is introduced to analyze the stability of the double-hole soil cave from three aspects, the lateral pressure coefficient, the ratio of the soil cave radius and the relative position of the soil cave. The results reveal that the stability coefficient of soil cave has a linear positive relationship with the lateral pressure coefficient. It decreases nonlinearly with the increasing value of the ratio of the soil cave radius and remains unchanged first and then increases linearly with the increase of the relative position of the soil cave.