Monte Carlo techniques are used to simulate magnetic properties of chains of identical, spherical, single-domain, ferromagnetic nanoparticles with cubic magnetocrystalline anisotropy. Nanoparticles are placed along a straight line with their positions and directions of anisotropy axes fixed in changing external magnetic field. Hysteresis curves as well as zero field cooled (ZFC) and field cooled (FC) experiments are simulated for chains of different lengths, i.e. differing in both: the number of particles and inter-particle distances. Strongly anisotropic dipole–dipole inter-particle interactions lead to significant differences in system’s response to the external magnetic fields oriented parallel and perpendicular to the chain, and further, to the occurrence of wasp-waisted hysteresis loops. We compare results for chains that differ in the size of particles they are built of. To get the idea about the quantitative scale of the discussed phenomena we assume values of magnetocrystalline anisotropy constants for fcc-Co.