The effect of thickness of spiral arms in the dynamics of normal spira
l galaxies is examined. We find stable 3D periodic orbits with ellipti
cal projections on the equatorial plane, which can support a spiral pa
ttern with variable thickness. It is shown, that in general these 3D o
rbits can be found even in models with strong forcing in the z-directi
on. Differences depending on disk scale lengths and heights as well as
on the disk/halo decomposition are outlined. The edge-on shapes of or
bits found in the thick spirals are associated with the vertical reson
ances existing in the potential. The structure of the stable families
of periodic orbits suggests that edge-on peanut-shaped profiles are as
sociated to the vertical resonances of the axisymmetric potential and
therefore can appear in all types of disk galaxies i.e. not only in sy
stems with a bar perturbation.