The existence of boiling phenomena in boiling water-reactors makes these systems susceptible to instabilities. Neutronics coupled with the thermal-hydraulics complicate the problem further Boiling water reactor instabilities are classified as global or local according to the spatial dependency of the power fluctuations. At present, numerical codes can simulate these instabilities rather well on event basis; but more general physical insight can be gained readily through analytical modeling. One of the earliest models applied to the problem is the parallel channel instability, so called because of the applied thermohydraulic boundary conditions. In this work a new type of instability model is proposed and studied by including the effect of the first axial harmonic of the flux. Thermal-hydraulics is represented with one-dimensional two-phase homogeneous equilibrium flow model equations. Analysis is performed with linearized equations in the frequency domain. Special emphasis is given to the motion of the boiling boundary. The results clearly indicate that the first axial harmonic of the flux affects the stability of the reactor adversely, and must be accounted for to make more realistic predictions.