A simple approach is developed in order to model the influence of collisions on the shape of infrared absorption by linear molecules. It accounts for line-mixing effects within, as well as between, the different branches (P,Q,R) of the band. It is based on use of the strong collision model, of a classical representation of rotational levels, and of the rigid rotor approximation. The absorption coefficient then has a very simple analytical expression; its wave number and pressure dependencies are computed by using eight parameters which depend on the considered vibrational transition, the temperature, and the nature of the perturber only. These quantities are band-averaged values of the detailed spectroscopic and collisional parameters of the molecular system. Tests of the model are presented in the nu(3) and 3 nu(3) bands of CO2 perturbed by He and Ar at elevated pressures. They demonstrate the accuracy of our approach in accounting for the effects of collisions on the spectral shape in a wide density range; indeed, the superposition of Lorentzian individual lines at low pressure, as well as the collapse (narrowing) of the band at very high pressure are satisfactory predicted.