Stokes flow separation past a spherical cap or a circular disc is studied for the axisymmetric case by means of flows generated by the following singularities: A Stokeslet, a Stokeslet dipole, a source and a dipole. We find that the flow separates at the rim of the cap or disc and when the singularity is far, the flow field is qualitatively similar for all singularities considered and has a separation bubble on the concave side of the cap or on the side of the disc shielded from the singularity. When the singularity is not very far from the cap or disc the structure of the flow field depends on the singularity. In the case of the cap, for instance, for a Stokeslet there is just one separation bubble which occurs on the convex or concave side of the cap depending on whether the Stokeslet is within or outside the sphere of the cap, whereas for a dipole either one, two or three bubbles are formed and the structure and location of these bubbles depend on the position of the singularity and the cap angle. Also there are configurations where the cap experiences no thrust.