A new class of analytic solutions to the problem of two-dimensional potential fnow is presented here. The method of solution has features of both direct and indirect solutions. The bodies about which flow is computed are semi-infinite and have forward regions that either are flat or consist of a circular arc, which may be convex or concave to the flow. Closed-form solutions are obtained for the surface velocity. Afterbody shapes are defined by implicit equations containing a quadrature. Certain analytic properties of the solutions are investigated. An interesting feature of the bodies is the presence of a ‘pseudo corner’ where the slope angle is continuous but the curvature is infinite. The surface velocity becomes logarithmically infinite at these points in contrast to the power-law behaviour at a true corner. One case of the convex circular arc has finite velocity everywhere, and in some sense represents flow over a circular cylinder with a ‘natural’ separation point. This point occurs at 77·45° from the front stagnation point, which is close to the separation point for incompressible laminar boundarylayer flow.