Platinum metal Ir-Rh alloy presents a promising candidate as future ultra-high-temperature gas turbine material due to its excellent high-temperature properties. In this paper, the mechanical properties of Ir-xRh (x=0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100) alloys with different rhodium content are investigated. Self-consistent, periodic, density functional theory calculations, Perdew-Burke-Ernzerhof functional, virtual crystal approximation are employed to calculate the elastic constants C11, C12, C44, Cauchy pressure (C12-C44), Young modulus E, shear modulus G, bulk modulus B and the ratio G/B, anisotropic factor A, and strain energy of dislocation per unit length. These parameters are adopted to characterize and assess the effect of Rh content on the mechanical property of Ir-Rh alloy. The results indicate that it is reasonable to use the virtual crystal approximation to calculate the mechanical properties of Ir-Rh alloys. The Young modulus E, shear modulus G and bulk modulus B increase rapidly with the increase of rhodium content, and the maximum value is reached at rhodium content 10%. Then it fast dereases down to a minimum value at 40% after the slowly rises and then slowly drops down. It is found to be in remarkable agreement with the strain energy of dislocation per unit length. This indirectly explains its changing trend. The Cauchy pressure (C12-C44), G/B value and the Poisson's ratio reflect the change of the brittleness of the alloy. Therefore, we can come to a conclusion: the addition of Rh can cause the brittleness of the Ir-Rh alloys. The value of the brittleness first increases and then decreases with the increase of Rh content, and its maximum value is reached at 50%. The charge densities and the densities of states of pure Ir, Ir-10Rh, Ir-50Rh and pure Rh are calculated and compared. At the same time, we also establish a 2 2 1 solid solution supercell structure of Ir-Rh alloy and calculate its differential charge density. The results show that in the Ir-Rh alloys exists a pseudo covalent bond, which leads to the abnormal mechanical properties. The pseudo covalent bond is not a metal bond nor a covalent bond but a kind of transition bond or a mixed type. Finally, the experimental results show that the calculation method is reasonable and it can play an important role in understanding the microscopic mechanism of the abnormal mechanical properties of Ir-Rh alloys.