The effective-mass Hamiltonian for indirect excitons in cubic semiconductors is solved. The approach used allows a physical interpretation of the various terms in the Hamiltonian thus making possible the introduction of simpler but equally accurate models. In particular, the "axial model" is described, which is very suitable for the investigation of various problems. The validity of this model is discussed and shown to depend on the relative strength of the electron anisotropy and of the hole anisotropy. By using rotation-group techniques the angular and the radial part in the exciton Hamiltonian are separated and the problem is reduced to a system of radial differential equations. All the experimentally observed exciton levels are calculated. A comparison with the results obtained by the perturbative approach is given and analytical expressions for the most relevant exciton states are obtained in the perturbative limit. Recent experimental data for Ge are analyzed and excellent agreement with our calculations is obtained. Comparison is also made for Si and GaP. The usefulness of the present approach for the treatment of other problems is discussed. © 1977 The American Physical Society.