The crystal structures, elastic and anisotropic properties of CH3NH3BX3 (B = Sn, Pb; X = Br, I) compounds as solar cell absorber layers are investigated by the first-principles calculations. The type and strength of chemical bond B-X are found to determine the elastic properties. B-X bonds and the organic cations are therefore crucial to the functionalities of such absorbers. The bulk, shear, Young's modulus ranges from 12 to 30 GPa, 3 to 12 GPa, and 15 to 37 GPa, respectively. Moreover, the interaction among organic and inorganic ions would have negligible effect for elastic properties. The B/G and Poisson's ratio show it would have a good ductile ability for extensive deformation as a flexible/stretchable layer on the polymer substrate. The main reason is attributed to the low shear modulus of such perovskites. The anisotropic indices AU, AB AG, A1, A2, and A3 show ABX3 perovskite have very strong anisotropy derived from the elastic constants, chemical bonds, and symmetry.