[en] We present a Monte Carlo routine to simulate the azimuthal distribution of pair production by linearly polarized high-energy γ-rays in the range between 50 MeV and 1 GeV. This routine incorporates a parametric function (introduced in a previous work) which, in principle, can describe the physical interactions between a linearly polarized γ-ray and the nuclear electric field. When the code is implemented and the results are analyzed, one observes that both coplanar and non-coplanar events are important in determining the spatial azimuthal distribution of the pair. Even when summing over polarization directions (to include non-polarized incoming rays) one can see differences between these results and those obtained by other Monte Carlo routines (like GEANT) which assume that all events are coplanar. These differences are most noticeable for low energies (around 50 MeV) and thus one should reconsider the validity in using only coplanar events for the low energies. We introduce our routine into the GEANT code and perform simulations with a geometrical set up similar to future missions of space-based γ-ray telescope. We conclude that it will be very difficult for these missions to detect γ-ray polarization