Functionally Graded Materials (FGMs) have been developed as super-resistant materials for propulsion systems and airframes of space-planes to reduce thermal stresses and increase protection from heat. Generally, failures of functionally graded materials involve two types of cracks, namely a surface crack propagating perpendicular to and an embedded crack along the boundary. In this paper, a functionally graded material strip containing a surface crack perpendicular to the boundary is considered. The graded region is treated as a large number of single layers, with each layer being homogeneous material. The problem is reduced to an integral equation and is solved numerically. Unlike most of existing researches, which considered only certain assumed material property distributions, the analytical model developed in this work can be used to study functionally graded materials with arbitrarily varied material properties.