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A B S T R A C TThe main purpose of the paper is to propose a numerical method for evaluation of J-integral in plates made of functionally graded materials (FGM) with sharp and blunt V-notches under Mode I loading. The material properties have been assumed to be varied exponentially along the specimen width (notch direction). Using the proposed method, the effect of material gradient on the J-integral for two cases of sharp and blunt Vnotches has been studied. The results have shown that in FGMs with sharp V-notches, the J-integral is not proportional to r 2λ1−1 . So, the parameter J L is path dependent. It has been observed that the material gradient has larger effect on the J-integral in sharp V-notch compared with that in blunt V-notch.Keywords FGM; J-integral; numerical method; V-notch.N o m e n c l a t u r e a = notch depth B = thickness of the specimen C = a multiplying factor D = distance of control volume boundary from notch boundary E = Young's modulus E(0,0) = Young's modulus of base point f ij = angular function in stress distribution F = applied load g ij = angular function in stress distribution J = J-integral J 1 = first term of J-integral J 2 = second term of J-integral J L = a path-independent J-integral in sharp V-notches J L1 = first term of the J L J L2 = second term of the J L K IC = fracture toughness K V I = Mode I notch stress intensity factor (N-SIF) n x , n y = unit normal vector of integration path q = parameter linked to the V-notch opening angle as defined in Fig. 1 r = polar coordinate R C = control radius R C,tip = control radius at the notch tip R 1 (θ ) = semicircular root of the notch S = span length in three-point bending specimens