A one-layer quasi-geostrophic model is used to study Taylor columns on both the f-plane and the β-plane in the inviscid limit of the frictional problem. In this limit, the fluid is stagnant within the Taylor column and the velocity vanishes on its boundary. Ingersoll (1969) found an analytic solution for such a Taylor column for flow over a right circular cylinder on the f-plane. Under more general circumstances, an analytic solution is no longer possible. In this paper, solutions are found numerically by solving an integral equation for the values of the stream function on the boundary of the Taylor column, and then iteratively solving for the shape of the boundary. Ingersoll's solution is first extended by finding the shape of the Taylor column for flow over a cone on the f-plane where the Taylor column has a tear drop shape. Solutions are also found for westward and eastward flow over a cylinder on the β-plane. The Taylor column is approximately elliptical for westward flow with the major axis in thexdirection, while it is slightly elongated in theydirection for eastward flow. For eastward flow, it is located north and west of where it was on the f-plane because of the asymmetry in the solution arising from the Rossby lee waves downstream of the topography. The stagnation point of the Taylor column is located on the edge of the topography for all the solutions found.