The melting curves of short sequences of DNA is solution are calculated on the basis of statistical thermodynamics. The computation of the partition function is based on the Peyrard-Bishop hamiltonian, which has already been adopted in the theoretical description of the melting of long DNA chains. We have adapted this model to short sequences, where it is necessary to consider also the complete dissociation of the two strands, contrary to the case of long sequences. We show a comparison with some experimental data.