The full-potential linearized augmented plane wave method with the generalized gradient approximation for the exchange-correlation potential (FLAPW-GGA) is used to predict the electronic and elastic properties of the newly discovered superconducting nanolaminate Ti2InC. The band structure, density of states and Fermi surface features are discussed. The optimized lattice parameters, independent elastic constants, bulk and shear moduli, compressibility are evaluated and discussed. The elastic parameters of the polycrystalline Ti2InC ceramics are estimated numerically for the first time.