A numerical approach for the analysis of quantum wire structures has been presented using a finite-element method which includes the strain analysis and the band analysis of the Luttinger-Kohn Hamiltonian with the deformation potential. A systematic implementation of the multiband Hamiltonian in the finite-element scheme is outlined and the corresponding variational functional is derived for arbitrarily shaped strained quantum wire arrays. This method is then applied to calculate the band structures of strained quantum wire arrays.