Grand canonical Monte Carlo results are reported for an electric double layer formed by a planar electrode and spherical ions. The non-electrostatic interactions are the soft interactions approximated by the Lennard-Jones (LJ) potential. In particular, the ion-ion interactions are described by the 12-6 LJ potential, while the ion-electrode interactions are given by the 9-3 potential. The ion charge is located at the centre of a sphere. Ions are immersed in a continuous dielectric medium whose relative permittivity is equal to that of a solvent. The results of simulations for a 1:1 electrolyte and the same ion diameters show that the singlet distribution function of counter-ions has a single high maximum, while that of co-ions has two small maxima. The maxima of counter- and co-ions increase with increasing ion-ion or ion-electrode soft interactions, with decreasing temperature or electrolyte concentration. Analogous changes in the soft interactions, temperature and electrolyte concentration lead to formation at some distance from the negatively charged electrode surface of a negative minimum of the integrated charge, which indicates the over-screening or charge reversion effect. They also transform the shape of differential capacitance curve from that having a maximum (bell-like shape) at the point of zero charge to that showing a minimum surrounded by maxima (camel-like shape). Difference in ion charges or in ion diameters introduce asymmetry in the shape of differential capacitance curves. Increase in a counter-ion charge (the absolute value) or decrease in their diameters elevate the electric double layer capacitance. (C) 2018 Elsevier Ltd. All rights reserved.