In the accumulation zone of glaciers and ice sheets snow is transformed into glacial ice by firn densification. Classically, this process is assumed to solely depend on temperature and overburden pressure, which is controlled by the accumulation rate. However, exceptionally thin firn layers have been observed in the high-strain shear margins of ice streams. Previously, it has been proposed that this firn thinning can be explained by an enhancement of firn densification due to the effect of strain softening inherent to power-law creep. This hypothesis has not been validated, and the greater firn densities in the presence of horizontal strain rates have not yet been reproduced by models. Here, we develop a model that corrects the firn densification rate predicted by classical, climate-forced models for the effect of strain softening. With the model it is confirmed that strain softening dominates the firn densification process when high strain rates are present. Firn densities along a cross section of the Northeast Greenland Ice Stream (NEGIS) are reproduced with good agreement, validating the accuracy of the developed model. Finally, it is shown that strain softening has significant implications for ice core dating and that it considerably affects the firn properties over wide areas of the polar ice sheet, even at low strain rates. Therefore, we suggest that, besides temperature and accumulation rate, horizontal strain rates should generally be considered as a forcing parameter in firn densification modeling.