Opening mode stress intensity factors are determined using point matching for two diametrically opposed radial cracks at a hole in a rectangular sheet v/here the cracks lie along the line of the minimum section. The sheet is subjected to either a biaxial stress on its edge or a pressure distribution on the hole boundary. The pressure on the hole is uniform or has a cosine distribution, symmetrical about the line of the cracks and having zero value on the crack-line. By applying the principle of superposition it is shown that the results can be applied to pin-loaded joints to determine stress intensity factors for different combinations of pin-load and interference fit and the effects of load transfer ratio between the pin or rivet load and the remote loading. Detailed results are given for stress intensity factors of cracks in a wide range of typical pin-joint configurations and it is shown that the stress intensity factors, for small cracks, are strongly dependent on the type of pressure distribution assumed to represent the pin-loading. Reducing the distance from the pin to the stress-free end of the joint is shown to increase the stress intensity factor more in the case of pin-loading than in the case of a uniaxial stress. The stress intensity factors, determined for simple lug-joints, are in agreement with available results from existing theoretical and experimental work and, for cracks at fastener holes, comparisons are made with other more approximate solutions.