The excitation of magnetostatic surface waves (MSSW) is formulated in terms of vector instead of scalar potential theory. The method is two‐dimensional and is suitable to handle the MSSW generation in any plane‐parallel film stack by striplines with predefined current distributions. The absorption due to the finite electrical conductivity and the Gilbert precession damping are accounted for. Both the real and imaginary parts of the radiation impedance are explicitly derived for a stack with one ground plane with finite electrical conductivity, located at finite distance from the magnetic film which possesses a Gilbert type of damping. One microstrip line is located between the magnetic film and the ground. Numerical results for these configurations are presented for a variety of parameters, such as stripline geometry, the ground‐plane conductivity, ground‐plane distance, and Gilbert damping constant.