This article proposes a new finite elements based three dimensional method developed to study the phenomenon of fatigue crack propagation in functionally graded materials (FGMs). The particular problem examined in detail is that of an initially-elliptical crack located in a functionally graded medium, subjected to mode I cyclic loading. The crack is modelled by employing three dimensional finite elements; and the stress intensity factors (SIFs) around the crack front are computed by the application of the displacement correlation technique (DCT). Fatigue crack propagation calculations are based on the Paris-Erdogan crack growth law. The developed procedure makes it possible to generate the crack front profiles corresponding to given numbers of loading cycles. Proposed methods are validated by examining the behaviours of both stationary and propagating cracks. Numerical analyses conducted for an initially-elliptical crack lying in a graded medium demonstrate that the proposed model can effectively capture the evolution of the crack front morphology. Hence, the methodology presented in this article can be used along with fracture toughness data to assess the fatigue lives of functionally graded components containing cracks that possess arbitrary front profiles. (C) 2011 Elsevier B.V. All rights reserved.