The capillary interaction among particles is an important aspect of analyzing the mechanical properties of wet granules. By considering the interaction between two spherical particles and the inter-particle meniscus, exact solutions for geometry and matric suction of the interface of gas-liquid-solid are deduced by shooting method. The results by the proposed method are compared with the inter-particle forces obtained by the annular approximation method and the data fitting method to evaluate the accuracy of the two simplified methods. The characteristic curves of the suction stress caused by the capillary action between the two spherical particles are analyzed for different inter-particle spacings, different liquid-solid contact angles and different matrix suctions. The results obtained by the fitting method are better for the smaller volume of the liquid, and the result by the circular approximation is closer to the exact solution than that by fitting method for larger liquid volume. This study provides some theoretical guidance for understanding the suction in unsaturated soils and microscopic analysis of unsaturated soil mechanics.