Atomistic modelling of Materials Science problems often requires the simulation of systems with an irreducibly-large unit cell, such as amorphous materials, fullerites, or systems containing extended defects, such as dislocations, cracks or grain boundaries. Large-scale simulations with the Tight-Binding approach must face the computational obstacle represented by the O(N
3)-scaling of the diagonalization of the Hamiltonian matrix. This bottleneck can be overcome by parallel computing techniques and/or the introduction of faster, O(N)-scaling algorithms. We report the activities performed in the frame of a collaboration among several research groups on the porting of TBMD codes on parallel computers. In particular, we describe the porting of a O(N
3) TBMD code on different MIMD computers, with either distributed or shared memory, by using appropriate software tools. Furthermore, preliminary results obtained in the porting of an O(N) TBMD code on an experimental, hybrid MIMD-SIMD computer architecture are reported. The new perspective of using specialized platforms to deal with large-scale TBMD simulation is discussed.