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The boundary element method is applied to the modelling of arbitrarily shaped surface which will be used for the design of antennas on these surfaces. The surfaces are approximated by planar linear triangles and the surface fields an expanded into series of either constant or linear shape functions. The unknown coefficients of the field expansion are calculated using a collocation technique. The application of linear shape functions is problematic on regions with small radii of curvature and at surface inhomogeneities. These problem stem from the singular surface integrals involving the linear shape functions times the gradient of the free space Green's function. The use of combined constant and linear shape functions in proposed in order to handle also the problematic cases. A numerical example is given.