A shelf edge model is used to examine the stability of an along shelf flow to changes in potential vorticity of the inflow. Calculations with a two-dimensional vertically integrated hydrodynamic model, (containing the nonlinear momentum advection terms), using different inflow jet positions and magnitudes show that barotropic instabilities in the along shelf flow can give rise to both stable and unstable shelf modes with associated eddies. The influence of the form of boundary condition, and horizontal viscosity term (parameterized using either a bi-harmonic or Laplacian operator) upon the solution is also examined. In initial calculations a large region model is used to produce a benchmark solution against which limited domain calculations can be tested and the sensitivity of the solutions to open boundary conditions assessed. Calculations are used to examine the influence of a range of inflow and outflow boundaries upon the accuracy of the solution. This involves comparing total solutions and results from an Empirical Orthogonal Function (EOF) analysis. The EOF analysis also yields significant insight into flow features. Comparisons show that Sommerfeld type outflow boundary conditions remain stable and cause very little false reflection provided the horizontal viscosity coefficient in the biharmonic formulation is increased close to the open boundary. In the case of an inflow that produces strong barotropic instabilities then the form of the inflow boundary can influence the solution. If a Laplacian rather than a biharmonic horizontal diffusion is used, then excessive smoothing can occur.