In this study, the band structures of conventional InAs/GaSb and M structure super lattices are investigated using the k.p method. First, the band structures of InAs/GaSb super lattices with various period thickness are calculated, and the period structure used for a longwave super lattice detector is obtained. Subsequently, the band structure of the M structure super lattice, which is prevalently employed in longwave super lattice infrared detectors, is also calculated. The band offset between a longwave InAs/GaSb super lattice and M structure super lattice is provided. Furthermore, based on the band structures, the relationship between the carrier density(doping density) and the position of the Fermi level for longwave InAs/GaSb and M structure super lattices is obtained. This was followed by a density of states (DOS) calculation. These calculated material parameters can provide the foundation for designing super lattice infrared detectors.