Old snow (denoted as firn) accumulates in the interior of ice sheets and gets densified into glacial ice. Typically, this densification is assumed to only depend on temperature and accumulation rate. However, it has been observed that stretching of the firn by horizontal flow also enhances this process. Here, we show how to include this effect in classical firn models. With the model we confirm that softening of the firn controls firn densification in areas with strong horizontal stretching.