**1. Introduction**

The macroscopic properties of the randomly organized media has attracted research interest for many decades. Nowadays, the the critical study points are the determination of the properties of composites filled with the carbonaceous fillers, like carbon nanotubes (CNT) [1–4], or graphene nanoplatelets (GNP) [5–8]. All these objects have high aspect ratios, and there is an interest to develop anisotropic composites using the partially oriented fillers [9–11]. There are several ways to reach the anisotropy in case of a CNT-filled composite, for instance: mechanical deformation, curing the CNT-filled polymer in external fields, or template-based techniques (see [12] and Refs therein).

Currently, there are different ways to model the macroscopic properties of carbon composites. Among them are: general effective media model [13], excluded volume theory [14], Monte Carlo models [15,16], finite and boundary element methods [17,18]. For the conductive properties modelling, the Monte Carlo based techniques are one of the most interesting due to their simplicity, extremely high tunability and good agreement with the experimental results (See [19] and Refs therein).

However, Monte Carlo models for the aligned CNT composites lack in several aspects. Firstly, many studies introduce the cut-off zenith angle as an anisotropy parameter (AP) and investigate the dependencies of the macroscopic properties on the cut-off values [20–22]. In case of the real systems, one can measure the deformation degree or the externally applied field, but not the cut-off angle. Secondly, there is some contradiction in conductivity data for the partially oriented composites. Many report on the descent of conductivity with the increase of the AP [22–24], and several demonstrate a maximum of the conductivity with the small values of the AP [20,21,25]. To figure out the conductivity dependence, the critical concentration dependence on the anisotropy parameters should be investigated. Finally, the properties of the aligned composite should be studied along different directions, while most of the studies usually report on the behaviour along one direction [21–23].

In this paper, the CNT-filled composite after mechanical deformation, which in our model is introduced as non uniformity in angular coordinate distribution, is investigated. The percolation threshold and conductivity are computed as a function of the mechanical deformation. Two main directions (along and perpendicular to the deformation axis) are studied.
