Digital waveguides may be used to construct efficient physical models of musical instruments and other resonant systems. They are commonly used to model systems with simple boundary conditions, such as strings and square membranes. Membranes are modelled by connecting digital waveguides together to form a mesh; however when modelling circular membranes, such as those found in percussive drums or microphones, the mesh does not approximate well to the boundary shape. It was found that a two-dimensional triangular mesh structure, with rimguides attached around the edge could overcome this. In this paper several rimguide strategies have been explored. The best of these involves adjusting the phase delay so that the model is accurate for frequencies close to DC. The improvement is particularly noticeable for efficient (low sample rate) implementations. (6 pages)