An analytic solution to a particular boundary value problem in linear elasticity is presented. The problem considered is that of a circular disc, in plane strain or generalized plane stress, which is loaded quite generally at the perimeter by a set of self equilibrating forces. The disc has a radial crack extending completely from the centre to the perimeter. Three particular load cases are considered: the disc is loaded by uniform radial tension; the disc is pulled by two diametrical concentrated loads with line of action perpendicular to the crack; the disc is pulled by two concentrated forces acting at the mouth of the crack. In each case the stress intensity factor is evaluated and contours of the isochromatics are presented in dimensionless form. The results agree with those derived by other workers but the method presented here is more general, more efficient, and extends the previous results for finite bodies containing cracks. The three load cases have also been applied to the disc when the tip of the crack has been removed by the presence of a concentric hole. New results are presented for the stress concentration factors for a full range of geometric parameters. Finally it is shown how the second and third of the load cases may be used for controlled laboratory tests in the study of fracture and fracture toughness of brittle materials.