A two-dimensional finite element groundwater flow model is used to study the flow into and out of large cavities created by underground coal gasification burns in a coal seam. The model uses linear triables to discretize the coal eam in plan and can handle unsteady flows, antostropic media, and the time-dependent boundary conditions imposed by the cavities. After a cavity is created the groundwater begins to flow into the cavity and raises the water level in it, until it fills up. During this phase, the boundary condition imposed is one of constant head at the boundary nodes of the cavity. When the cavity is filled, groundwater flows through the cavity into the coal seam, with the conductivity in the cavity much larger than that in the seam. Either before or after the filling of the cavity, a new caity may be created by UCG burns in adjacent locations of the seam. The program is designed to handle any number of successive burns that may occur. The model has been applied to the UCG burns at the Hanna site in Wyoming. Maps of constant piezometric head in the coal seam simulated by the model at different times have been prepared and compared with similar maps of measured piezometric head.