Elastic and elastic-plastic analyses of a crack in a particulate-dispersed functionally graded material (FGM) have been carried out using a newly developed finite element method based on Tohgo-Chou-Weng's (1994, 1995) constitutive relation for particulate-reinforced composites. By setting the mechanical properties of particles and a matrix and their contents graded in the thickness direction, graded and non-graded materials are designed. From comparison of the numerical results for the graded and non-graded materials, the influence of the gradient of the mechanical properties on a stress intensity factor and the crack-tip field is discussed. The following conclusions are derived : ( 1 ) The stress intensity factor of a crack under constant boundary conditions is considerably affected by the gradient of the mechanical properties. ( 2 ) The elastic and plastic stress singular fields around a crack-tip in a FGM are basically described by the fracture mechanics parameters (KI and JI) as well as in a non-FGM, using the mechanical properties of the material at the crack tip. ( 3 ) The size of the singular field decreases with an increase in the gradient of the mechanical properties. This means that the applicability of fracture mechanics, such as the small-scale-yielding condition and the validity of the J-integral, is affected by the gradient.