Although tricalcium aluminate (C(3)A) is one of the most important components of Portland cement, neither its reactivity nor its elastic moduli tensor have been fully determined yet. This work aims to shed some insights on these questions by means of ab-initio simulations. First our simulations have reproduced the details of its crystalline structure. Second, we have computed the full elastic moduli tensor of C(3)A, where we found that our value for the Young modulus (E=138.7 GPa) is in agreement with the values obtained by nanoindentation measurements. Finally, we have identified which atoms and sites are more suitable to suffer chemical attacks.