We present a systematic study of the stability of nineteen different periodic structures using the finite range Lennard-Jones potential model discussing the effects of pressure, potential truncation, cutoff distance and Lennard-Jones exponents. The structures considered are the hexagonal close packed (hcp), face centred cubic (fcc) and seventeen other polytype stacking sequences, such as dhcp and 9R. We found that at certain pressure and cutoff distance values, neither fcc nor hcp is the ground state structure as previously documented, but different polytypic sequences. This behaviour shows a strong dependence on the way the tail of the potential is truncated.