Advective flows within soils and snowpacks caused by pressure fluctuations at the upper surface of either medium can significantly influence the exchange rate of many trace gases from the underlying substrate to the atmosphere. Given the importance of many of these trace gases in understanding biogeochemical cycling and global change, it is crucial to quantify (as much as possible) any impact these flows can have on the transport of these gases. This study (part 1 of 2) details a new model describing the influence that naturally occurring, pressure-driven, oscillatory advective flows have on CO₂ profiles within soils and snowpacks and on the associated CO₂ fluxes emanating from the underlying source. This model, which consists of two layers with differing permeability and CO₂ source strength, is developed for both a dispersive and a nondispersive medium. The pressure forcing and the CO₂ response, modeled as plane waves in time and the horizontal direction, have amplitudes that vary in the vertical direction as described by analytical solutions to the diffusion equation (for pressure) and the advective-diffusive and dispersive-diffusive equations (for CO₂). In the case of a dispersive medium, the dispersion coefficient is derived in terms of the horizontal wave number and amplitude of the pressure forcing at the upper surface and the vertical structure and dispersivity of the medium. Diffusive flux enhancement factors, developed for the dispersive and nondispersive models, are expressed as functions of the surface amplitude of the pressure forcing, the permeability and cross-sectional shape and dimension of the pore tubes of the medium, and the vertical structure of the medium. Results indicate that advective flows induced by naturally occurring atmospheric pressure fluctuations are likely to enhance diffusive fluxes more in a dispersive medium than a nondispersive medium. However, such pressure forcing can significantly enhance diffusive fluxes in either medium.