Using first-principles calculation we investigated the structural, electronic and elastic properties of paramagnetic CaFeAs2. Our results indicated that the density of states (DOS) was dominated predominantly by Fe-3[Formula: see text] states at Fermi levels, and stronger hybridization exists between As1 and As1 atoms. Three hole pockets are formed at [Formula: see text] and Z points, and two electronic pockets are formed at A and E points. The Dirac cone-like bands appear near B and D points. For the first time we calculated the elastic properties and found that CaFeAs2 is a mechanically stable and moderately hard material, it has elastic anisotropy and brittleness, which agrees well with the bonding picture and the calculation of Debye temperature ([Formula: see text]).