Numerical modeling of energy levels and corresponding wave functions of exciton states in heterostructures with GaAs/Al(formula presented)Ga(formula presented)As quantum wells of different widths is performed. The modeling is based on an accurate finite-difference solution of the time-independent three-dimensional Schrödinger equation. A dependence of energy levels on a quantum well width as a parameter is studied. The calculated exciton states are classified according to their quantum-confinement and Coulomb nature. The radiative decay rates of the modeled states are also obtained.