An analytical method has been developed to determine the state of three-dimensional stresses in a sphere subjected to multiple contact loads. The method has been used to study the stress distribution in a sphere under a variety of loading conditions important to particulate systems. It is found that in the case of three-point in-plane loading the maximum tensile stresses are larger than that in uniaxial compression. As the number of contact points increases, the maximum internal tensile stress, in general, decreases as the state of stress inside the sphere approaches hydrostatic compression. The method was used to analyze the stresses in some tests carried out on glass and alumina spheres. The stress analysis indicates that the maximum contact stress and hence the tensile stress outside the contact circle correlate well with failure and are partially responsible for attrition in particulate systems.