Abstract: In this work, we model the polarisation of the auroral red line using the electron impact theory developed by Bommier et al (2011). This theory enables the computation of the distribution of the Degree of Linear Polarisation (DoLP) as function of height if the flux of precipitated electrons is provided as input.\\
An electron transport code is used to infer the stationary electron flux at each altitude in the ionosphere as a function of energy and pitch angle. Using adequate cross sections, the integral of this electron flux over energy and pitch angle provides an anisotropy parameter from which the theoretical local DoLP can be computed at each altitude. The modelled DoLP is then derived by integrating along the line-of-sight.\\
Depending on the integration length, the modelled DoLP ranges between 0.6\% for a very long integration length, and 1.8\% for a very short integration length localized around an altitude of 210 km. A parametric study is performed to check how the characteristics of the local DoLP (maximum value, altitude of the maximum, integrated height profile) vary. It is found that the polarisation is highly sensitive to the scattering function of the electrons, to the electron precipitation and the geomagnetic activity.\\
We compare these values to measured ones obtained during an observational campaign performed in February 2012 from Svalbard. The measured DoLP during the campaign was 1.9\% $\pm$ 0.1\%. The comparison between this value and the theoretical one is discussed . Discrepancies may be due to the poor constraint of the input parameters (thermosphere and ionosphere), to the fact that only electron precipitation is considered in this approach (and not proton precipitation for instance), and to the difficulty in constraining the exact width of the emission layer in the thermosphere.