A general theory of spectral band shapes for molecular gases taking into account line mixing and collision duration effects was developed in kinetic equation approach. The expressions for a band shape are obtained in Markovian limit, their limits of application being determined. The band wing shape is related to the molecular torque spectrum. The band wing intensity is proved to depend on the structure of the relaxation matrix. The basic relations of the general bandshape theory are used to develop methods of atmospheric tranmission function calculation. An effective calculation method is proposed which is based on the adjusted branch coupling (ABC) model for vibration-rotation bands. In such calculation, the degree of branch coupling is determined by a single adjustable coefficient Cb. The other parameters are taken from the known atmospheric HITRAN database. The method is tested for the treatment of laboratory IR spectra of several molecules (CO2, O3, CH3F, CH4). The method is compared with that of Rosenkranz. The ABC model proved to be more flexible and to predict much better the bandshape in the wings, being in average as accurate as the Rosenkranz method is. Various transmission function calculations are performed for different absorption bandshapes of CO2, O3, CH4. Line mixing is proved to influence essentially on transmission functions on tangent paths. There are estimated spectral regions and heights sensible for the effect.