Geometry effect on the magnetic susceptibility of vertically coupled quantum rings (VCQRs) with three shapes of structure is numerically investigated. The theoretical model of VCQRs considers a three-dimensional effective one-electronic-band Hamiltonian with the position- and energy-dependent effective mass, the finite hard-wall confinement potential, and the Ben Daniel-Duke boundary condition. With the nonlinear iterative method, the model is solved with respect to the disk-, elliptical-, and triangular-shaped VCQRs under applied magnetic fields. For nanoscale InAs/GaAs quantum rings, electron transition energy depends on the shape and size of VCQRs; it oscillates non-periodically among the lowest electron states as a function of external magnetic fields due to the penetration of magnetic fields into the inter-regions of VCQRs. Non-periodical oscillating magnetization results in that the differential susceptibility has delta-like paramagnetic peaks. The peak depends on the geometry of structure which is contrary to conventional mesoscopic arguments. Recent development of spintronics requires an extensive study of magnetic properties of nanoscale semiconductor structures. This study provides interesting results for the magneto-optical phenomena of the nanoscale semiconductor artificial molecules.