A Stress Intensity Factor (SIF) Mode I is calculated for longitudinal composite plate with dimensions (104 mm × 40 mm) and fiber volume fraction (37.5%).The finite element method (FEM) (ANSYS) and MFree method are used for calculating the SIF of quarter model (i.e. (52 mm × 20 mm)) with constant displacement in ydirection that is applied at the ends of the plate. The crack length, material properties of fiber and material properties of matrix affect the SIF and these parameters are studied to understand the crack growth and the fracture mechanism in composite material. The value of SIF depends on the position of crack tip in additional to the material properties of fiber and matrix. A comparison between the FEM and MFree method is made to study the advantages and disadvantages of each method and to choose the suitable method for calculating SIF for composite plate. Generally, there is a good agreement between the FEM and MFree method but there is a slightly difference between them specially when the crack length increases. This slight difference happens due to the calculation technique of SIF used in each method. This difference makes the FEM accurate than the MFree method unless increasing the number of nodes around the crack tip in MFree method.