Fracture of perfectly oriented polymer fibres was studied by means of a computer simulation technique based on the ultimate structure model in order to estimate the upper limit of the tenacity of polymers with finite molecular weight. The fracture mechanism was also investigated in terms of average molecular weight and different nature of interchain interaction. It was observed that the tenacity of the model fibres increased with molecular weight and tended to approach the theoretical limit for the infinite molecular weight. In the cases of lower molecular weight, significant broadening of the stress distribution was observed under elevated stress, and the fracture behaviour was plastic. In the cases of higher molecular weight, the stress distribution was quite narrow until significant number of bond-cleavages occurred, and the fracture was brittle. The primary factor of fracture was found to be the chain-slippage in the lower molecular weight cases, and chain-scission in the higher molecular weight cases. Higher tenacity was marked when the polar interactions were introduced, especially in lower molecular weight cases. This can be attributed to the enhancement of chain binding by the polar interactions and suppression of chain-slippage.