We propose a simple acoustic model explaining the main features of gas chimneys. The main elements of the model consist of gas diffusing from a connected fracture network and into the surrounding shale creating an inhomogeneous gas saturation. The gas saturation results in an inhomogeneous fluctuating compressional velocity field that distorts seismic waves. We model the fracture network by a random-walk process constrained by maximum fracture length and angle of the fracture with respect to the vertical. The gas saturation is computed from a simple analytical solution of the diffusion equation, and pressure-wave velocities are locally obtained assuming that mixing of shale and gas occurs on a scale much smaller than seismic wavelengths. Synthetic seismic sections are then computed using the resulting inhomogeneous velocity model and shown to give rise to similar deterioration in data quality as that found in data from real gas chimneys. Also, synthetic common-midpoint (CMP) gathers show the same distorted and attenuated traveltime curves as those obtained from a real data set. The model shows clearly that the features of gas chimneys change with geological time (a model parameter in our approach), the deterioration of seismic waves being smallest just after the creation of the gas chimney. It seems likely that at least some of the features of gas chimneys can be explained by a simple elastic model in combination with gas diffusion from a fracture network.