Abstract Within the effective-mass approximation we introduce a transformed hamiltonian for the acceptor problem in a homogeneous magnetic field. The new hamiltonian is expressed entirely in terms of spherical tensor operators. The reduced-matrixelement technique can thus be used in solving variationally the eigenvalue problem. In this way a simple non-perturbation numerical calculation of the Zeeman split acceptor states becomes for the first time feasible. As a preparatory test for the method we used the new hamiltonian in a variational “model” calculation with a very restricted basis set, to calculate the linear Zeeman parameters for some excited states of shallow acceptors in Ge and GaAs. The results can be compared with recent experimental data for these materials. We find already an excellent numerical agreement between the calculated and the measured linear Zeeman parameters for the final states of the D-transitions, and we obtain the correct order of magnitude for those of the C-line final states.