The cold dark matter ( CDM ) scenario generically predicts the existence of triaxial dark matter haloes which contain notable amounts of substructure .
However , analytical halo models with smooth , spherically symmetric density profiles are routinely adopted in the modelling of light propagation effects through such objects .
In this paper , we address the biases introduced by this procedure by comparing the surface mass densities of actual N-body haloes against the widely used analytical model suggested by Navarro , Frenk and White ( 1996 ) ( NFW ) .
We conduct our analysis in the redshift range of 0.0 - 1.5 .

In cluster sized haloes , we find that triaxiality can cause scatter in the surface mass density of the haloes up to \sigma _ { + } = +60 \% and \sigma _ { - } = -70 \% , where the 1- \sigma limits are relative to the analytical NFW model given value .
Subhaloes can increase this scatter to \sigma _ { + } = +70 \% and \sigma _ { - } = -80 \% .
In galaxy sized haloes , the triaxial scatter can be as high as \sigma _ { + } = +80 \% and \sigma _ { - } = -70 \% , and with subhaloes the values can change to \sigma _ { + } = +40 \% and \sigma _ { - } = -80 \% .

We present an analytical model for the surface mass density scatter as a function of distance to the halo centre , halo redshift and halo mass .
The analytical description enables one to investigate the reliability of results obtained with simplified halo models .
Additionally , it provides the means to add simulated surface density scatter to analytical density profiles .
As an example , we discuss the impact of our results on the calculation of microlensing optical depths for MACHOs in CDM haloes .