Valence subbands of uniaxially stressed GaAs-Ga1-xAlxAs quantum wells are found by solving exactly the multiband effective-mass equation for the envelope function; as in the particle in a box problem, we first solve the effective-mass equation in each bulk material, and then we impose boundary conditions on the linear combinations of bulk solutions. Discrete symmetries of the effective-mass Hamiltonian are used to decouple the spin-degenerate subbands; the energy levels are obtained as the zeros of an 8Ã—8 determinant. The functional form of the wave functions is given analytically, and is used in order to discuss the heavy-hole light-hole mixing at finite values of the in-plane vector k?; the mixing greatly increases when the applied stress reduces the energy separation at k?=0. Resonances are shown to arise and are due to the degeneracy of discrete levels with states of the continuum at different values of k?. Â© 1987 The American Physical Society.