Boiling water reactor dynamic behavior is most sensitive to pressure variations at atmospheric pressure due to the strong dependence of saturation temperature on pressure. The two important pressure variation effects at atmospheric pressure are the variation of hydrostatic pressure within the core, which leads to a change in saturation temperature with position, and the pressure variations resulting from the acceleration of water by changing steam volume. A system of equations which takes into account these pressure effects in a natural circulation boiling water reactor is derived by means of conservation principles stated in integral form. The resulting equations are solved numerically. Sample calculations reveal no special tendency toward instability other than a form of hydraulic instability which does not depend on the inclusion of pressure effects in the model.