CuCrZr alloy (Cu-0.8wt-%Cr-0.1wt-%Zr) and 316L stainless steel (Fe-0.03wt-%C-16wt-%Cr-10wt-%Ni) plates were successfully friction stir lap welded resulting in significant mechanical mixing of the two matrix elements, Cu and Fe, in the stir zone. The severe mixing not only led to improved load bearing response but also leads to form Cu-rich and Fe-rich regions in the weld nugget. The formation of these phases governs the failure mechanism of the joint. Tensile properties of the weld showed promising response when compared with joints made for the similar alloy pair by other welding techniques. This suggests strong feasibility of applying FSW for joining Cu and steel for nuclear applications.