A 2-D model of stress distribution within bulk solids, with circular arc principal stress orientation, in a wedge hopper was developed in a previous paper [Matchett, O'Neill, & Shaw, Stress distributions in 2-dimensional, wedge hoppers with circular arc stress orientation - a co-ordinate-specific Lame-Maxwell model, Powder Technology, 187(2008) 298-306]. This model worked in an orthogonal, curvilinear co-ordinate system coincident with the principal stress trajectories: (x - psi(o)) space. This paper presents an equivalent model in (x - epsilon) space. This allows backward numerical integration of the force balance equations, enabling surface and wall boundary conditions to be modelled. This was not possible in the original model. The equations are first-order, and boundary conditions can only be specified at single surfaces. Thus, if a stable, cohesive arch is proposed, the surface overpressure is determined by the model. Calculated overpressures have reasonable physical values. The present model was integrated backwards from the surface downwards and it was found that the integration was very sensitive to the surface overpressure stresses. Likewise, wall boundary conditions were specified with backwards integration in epsilon. The minimum outlet for flow was calculated from the model and compared with the experimental data of Berry et al. Wall normal stresses in a wedge hopper from Schulze and Schwedes were also compared to model predictions. In both cases there was reasonable agreement between measurements and model predictions. (C) 2009 Elsevier B.V. All rights reserved.