The analysis of unconfined seepage flows is often required in geotechnical engineering, for instance when dealing with the design of earth dams, with the stability analysis of natural slopes, etc. They belong to the class of boundary value problems involving differential equations on a domain part of whose boundaries is unknown and has to be determined, together with the distribution of hydraulic head, as part of the solution. In the paper the equations governing the seepage flows, and the relevant boundary conditions, are first recalled both for the continuum problem and for its finite element discretization. Then, some variable and fixed mesh procedures for steady state and transient analyses are outlined. Some comments are also presented on solution approaches based on the so called "conformal mapping" technique. Finally the sources of instability which might affect the variable mesh approaches are discussed and a procedure is discussed aimed at avoiding these negative effects
