  The Murchison Widefield Array (MWA), located in Western Australia, is one of
the low-frequency precursors of the international Square Kilometre Array (SKA)
project. In addition to pursuing its own ambitious science program, it is also
a testbed for wide range of future SKA activities ranging from hardware,
software to data analysis. The key science programs for the MWA and SKA require
very high dynamic ranges, which challenges calibration and imaging systems.
Correct calibration of the instrument and accurate measurements of source flux
densities and polarisations require precise characterisation of the telescope's
primary beam. Recent results from the MWA GaLactic Extragalactic All-sky MWA
(GLEAM) survey show that the previously implemented Average Embedded Element
(AEE) model still leaves residual polarisations errors of up to 10-20 % in
Stokes Q. We present a new simulation-based Full Embedded Element (FEE) model
which is the most rigorous realisation yet of the MWA's primary beam model. It
enables efficient calculation of the MWA beam response in arbitrary directions
without necessity of spatial interpolation. In the new model, every dipole in
the MWA tile (4 x 4 bow-tie dipoles) is simulated separately, taking into
account all mutual coupling, ground screen and soil effects, and therefore
accounts for the different properties of the individual dipoles within a tile.
We have applied the FEE beam model to GLEAM observations at 200 - 231 MHz and
used false Stokes parameter leakage as a metric to compare the models. We have
determined that the FEE model reduced the magnitude and declination-dependent
behaviour of false polarisation in Stokes Q and V while retaining low levels of
false polarisation in Stokes U.
