Profiles of the electric field strength |E|2/|E0|2 for spherical metallic shells on a dielectric core are presented both inside the particle and outside. The dependence of the near-field strength and extent on shell thickness and total particle size is discussed qualitatively. Although the internal fields inside the shell and in the core are larger than for homogeneous particles, for not too thick shells, this does not translate into a stronger near-field away from the surface of the shell. The fields inside the shell, at the low energy resonance and close to it, are rotated by π/2 with respect to fields inside homogeneous particles, which means that the maximum field strengths in the shell are perpendicular to the incident polarisation. This follows from the fact that the low energy resonance for a shell is for the largest dipole moment of the whole system, which compensates the incident field. The largest moment is created when the same charges are collected at both interfaces (shell/medium and core/shell) along the incident polarisation. This creates regions of low field densities at the poles along the incident polarisation, because same charge fields repel each other. Following from that, the field lines are bunched up at the perpendicular poles, creating large field line densities and hence large fields at these points. The case for opposite charges across the interfaces creates the high energy, antisymmetric resonance.