An analysis method for the electromagnetic scattering of a gaussian beam wave by finite periodic conducting strip grating on a groudned dielectric slab is considered. The intergral equation for the unknown current induced on the conducting strip surface is derived and solbed numerically by use of the method of moment. From knowledge of the strip current, the quantities of interest such as radiation pattern, the space wave power radiated into the free space, and the coupled surface wave power propagating along the dielectric slab are computed for the appropriately chosen parametes Some similarity between scattering behaviours of the present geometry and the infinite geometry is examined by observing the Off-bragg as well as bragg blaxing penomena in both geometries.The validity of the numerical results are assured by a check of the power conservation relations.