We have studied the exciton states in vertically stacked self-assembled quantum disks within the effective mass approximation. The energy spectrum of the elect ron and hole is calculated using the transfer matrix formalism in the adiabatic approximation. The Coulomb interaction between the electron and the hole is trea ted accurately by the direct diagonalization of the Hamiltonian matrix. The effe ct of the vertical alignment of the disks on the ground energy of heavy- and li ght-hole exciton is presented and discussed. The binding energy is discussed in terms of the probability of the ground wave function. The ground energy of heav y- and light-hole excitons as a function of the magnetic field is presented an d the effect of the disk size (the radius of disks) on the exciton energy is dis cussed.