A direct solution procedure formulated is capable of coupling finite element and boundary element methods for the case of nonlinear potential flow. Nonlinearity between discharge and driving hydraulic gradient is anticipated to result from the onset of turbulent flow conditions within the fissure. The nonlinear portion of the domain is discretised using quadrilateral finite elements. A direct boundary element procedure is used to represent the linear behaviour of the far field. The coupled formulation is validated against analytical solutions for both linear and nonlinear axisymmetric flow in a single fissure and illustrated to perform satisfactorily. (Edited author abstract. )