The anisotropic mechanical properties of Tl4Ag18Te11 compound was investigated elaborately for the first time by using Density Functional Theory calculations with the Vienna Ab-initio Simulation Package in this work. Tl4Ag18Te11 compound was optimized in the I4mm space group and the formation energy was determined as a negative value that is the indication of the experimental synthesizability of this compound. The optimized crystal structure was employed for the calculations of the elastic constants and the obtained values revealed the mechanical stability of Tl4Ag18Te11 compound. The polycrystalline properties were determined such as shear modulus, Poisson's ratio, etc. In addition, the anisotropic elastic properties were presented. The direction dependent sound waves velocities, polarization of the sound waves, enhancement factor and the power flow angle were determined. The thermal conductivity studies were performed and the minimum thermal conductivity (0.259 W m(-1)K(-1)) and the diffusion thermal conductivity (0.202 W m(-1)K(-1)) were calculated. This study illustrates the capability of this compound for the thermoelectric materials.