In order to solve the stress of the surrounding rock with tubular double-ellipse caves under internal high water pressure, a plane stress model for double-ellipse caves under mixed boundary condition is employed in this study. Based on the plane elastic complex variable theory, two analytical functions of the plane stress containing internal water pressure with one elliptical cave are solved by means of conformal mapping, Cauchy integral and residue theorem. Using the Schwarz’s alternating method, the analytical expressions of component stresses in unlimited plane with two elliptical caves are obtained. According to these obtained expressions, Matlab software is applied to analyze four examples of stress in unlimited planes with two circular caves or two elliptical caves. The influences of internal pressure and the relative locations between two caves on the stress of surrounding rock are investigated. The results show that when two elliptical caves without internal pressure are arranged horizontally symmetrical, the maximum tangential orifice stress is found at 0° of left cave (or 180° of right cave). When internal pressure increases, both the maximum and minimum tangential orifice stresses decrease; if only one of these two caves containing internal pressure, when this pressure increases, the change of tangential orifice stress depends on its location relative to cave wall.