Friction Stir Welding (FSW) is a solid state joining process primarily used for Al alloys. Friction Stir Plug Welding (FPW) is a process in which a tapered shaped plug is friction stir welded into the hole that was left in the welded part when the initial FSW tool was removed. A rectangular plate made of Al 2195 alloy with a friction welded plug and containing a semi-elliptical surface crack was analyzed using the help of the software `FEA Crack'. Three different crack depths of deep cracks as well as shallow cracks were considered in identical plates of a quarter inch thickness. The depths were 0.08, 0.13 and 0.18 inches for deep cracks and 0.008, 0.013 and 0.018 inches for shallow cracks. A uniaxial tensile load of 1 psi was applied on one end surface with the opposite surface being fixed. For each depth, four different crack arc lengths were considered which were of 15, 30, 60 and 90 degrees. For each of these cases, the crack tube containing the crack was rotated around the plug having an inner bevel, in steps of 10 degree starting from the base position to the 90 degree (vertical) position with an additional case of 45 degree rotation in between. The stress intensity factor K was plotted against the crack front angle. The average and maximum K factor values were also plotted for each of the main crack lengths against the crack rotation angle. The same procedure was employed for shallow cracks. The results were validated using Newman-Raju equations for semi elliptical surface cracks. Non dimensional K factor plots were also made for different cases of both deep and shallow surface cracks. Researchers studying the surface cracks can now get an estimate of the value of stress intensity factor for the crack length, depth of crack and also the angular position of the crack around the plug by interpolating my results.