Most extant flow models for ocean ridges suffer either from unrealistic geometry (vertical conduit models) or a stress singularity at the ridge axis (corner flow models). I present a model which avoids these difficulties by incorporating a weak ''plate boundary zone'' (PBZ) between diverging surface plates. An analytical solution for the flow of a constant-viscosity asthenosphere and a coexisting melt phase is obtained in elliptic coordinates, and used to predict the dynamically supported topography (axial valley) on the PBZ, the force required to pull the plates apart, and the rate of melt extraction at the ridge. Stress in the asthenosphere increases linearly with spreading rate, but decreases as the plates become thinner, and the dynamics of ridge crests is controlled by the balance between these opposing effects. The depth of the axial valley is controlled by the plate thinning effect, and is therefore a decreasing function of spreading rate. The depth of the axial valley on the mid-Atlantic ridge can be explained if the viscosity of the asthenosphere is 6¿1019-1021 Pa s and the lower surface of the plate is the 600 ¿C isotherm. The plate separation force is controlled by the spreading rate effect and therefore increases with spreading rate. About five times as much force is required to maintain a fast spreading ridge (9 cm yr-1 half rate) as a slow spreading ridge (1 cm yr-1). Melt extraction can produce 6 km of basaltic crust if the volume fraction of melt present in the asthenosphere (≪total degree of melting) ranges from about 2.5--4.0% for a slow spreading ridge to 4.0--6.5% for a fast spreading ridge. The dynamics of melt extraction does not depend significantly on the finite width of the PBZ. ¿ American Geophysical Union 1988