  We derive a model for Sunyaev--Zel'dovich data from a galaxy cluster which
uses an Einasto profile to model the cluster's dark matter component. This
model is similar to the physical models for clusters previously used by the
Arcminute Microkelvin Imager (AMI) consortium, which model the dark matter
using a Navarro-Frenk-White (NFW) profile, but the Einasto profile provides an
extra degree of freedom. We thus present a comparison between two physical
models which differ only in the way they model dark matter: one which uses an
NFW profile (PM I) and one that uses an Einasto profile (PM II). We illustrate
the differences between the models by plotting physical properties of clusters
as a function of cluster radius. We generate AMI simulations of clusters which
are \textit{created} and \textit{analysed} with both models. From this we find
that for 14 of the 16 simulations, the Bayesian evidence gives no preference to
either of the models according to the Jeffreys scale, and for the other two
simulations, weak preference in favour of the correct model. However, for the
mass estimates obtained from the analyses, the values were within $1\sigma$ of
the input values for 14 out of 16 of the clusters when using the correct model,
but only in 6 out of 16 cases when the incorrect model was used to analyse the
data. Finally we apply the models to real data from cluster A611 obtained with
AMI, and find the mass estimates to be consistent with one another except in
the case of when PM II is applied using an extreme value for the Einasto shape
parameter.
