This paper presents a powerful approximate method for modelling the steady single-phase flow into a horizontal well completed with an Inflow Control Device (ICD) in an anisotropic reservoir. Two types of problems are investigated: the forward problem, which allows the user to find the flux distribution along the wellbore for a specified pressure drawdown, and the inverse problem to determine the ICD properties when the flux or reservoir pressure drawdown along the wellbore is given. The method is based on structuring the flow patterns around and, inside the wellbore and across the ICD and on the reduction of the dimensionality of the problem by using boundary integral equations. The resulting one dimensional singular nonlinear integro-differential equation is solved numerically, using the appropriate quadrature formula for singular integrals with Cauchy kernels.