This model is designed to simulate the temporal response of an ice sheet along a flow line by accounting properly for the division of the driving stress Into basal-stress and longitudinal-stress gradient components. A vertical section along a central flow line is divided into both horizontal and vertical grid points. A self-consistent solution of stress and velocity is found for any specified geometry. The sliding velocity is determined from a relationship which includes the base stress and a prescribed sub glacial water pressure. In these experiments, the ice is assumed to be isothermal. For any given set of initial conditions and a specified mass-balance distribution, the model follows the temporal behavior of the flow line to a steady state. In later work, the water pressure will be calculated from the equilibrium pressure within RothHsberger conduits for the specific geometry and determined rate of meltwater production. The time-varying temperature field due to conductive and advectlve processes will be included in later versions of the model.