The analytical and numerical formulation of the boundary integral equation (BIE) method are outlined for the general case in linear elasticity. Using this method, three-dimensional linear elastic fracture mechanics analyses of a rotating disc with a corner crack at its bore are carried out. The cases considered are for a disc with external to internal radius ratio of 8 and with thickness equal to the diameter of the central bore. Two different crack shapes, namely, a quarter-circular crack and a quarter-elliptical crack with ellipse aspect ratio of 0.75, are analysed. For each of these shapes, corner cracks penetrating 50 per cent and 75 per cent of the disc thickness are treated. Stress intensity factor solutions for these cracks are presented for the centrifugal loading condition, as well as when the disc is subjected to a radial tensile stress at its external circumferential periphery.