This is the second of a series of three papers which consider the correct formulation of the steady state and time-variant flow to tile drains. The first paper is concerned with steady state conditions and provides important information about the correct formulation of tile drainage. This paper examines the complex problem of the time-variant flow conditions associated with tile drains operating under atmospheric pressures. A brief review of the literature which considers the available time-variant methods of design of tile drains is given. The correct formulation of two-dimensional time-variant flow, which represents the tile drain as an internal boundary conditions separate from the water table, is developed. A method of representing the time-variant water table on a finite difference mesh is presented and the methodology is demonstrated by a typical problem. Comparisons are made with the United States Bureau of Reclamation (USBR) time-variant method of tile drain design.