This paper investigates the stress intensity factors of two penny-shaped cracks with different sizes in a three-dimensional elastic solid under uniaxial tension. The two cracks are symmetrically parallel located in the isotropic solid. Based on Eshelby's equivalent inclusion method and the superposition principle of the elasticity theory, a closed-form analytical elastic solution for the stress intensity factors (SIFs) on the boundaries of the cracks is obtained when the center distance between the two cracks is much larger than the crack sizes. A numerical method is employed to extract the solution for small center distance case. It is found that, due to the interaction between the two cracks, the first and second kinds of SIFs exist at the same time even if the applied stress is pure tension. Numerical examples are given for different configurations and it is clearly shown that the SIFs are strongly determined by the distance between the centers of the two cracks.