We present a theoretical study of the sum frequency generation (SFG) for the ammonia molecule adsorbed on the MgO(100) surface. This particular system could be a model for experimentalists in order to test this nonlinear technique, mainly for two reasons. First, the ammonia molecules can be considered in a first approximation as isolated on the surface due to repulsive lateral interactions. Second, the symmetry of ammonia and its particular equilibrium configuration on this surface allow us to separate the SFG response in a part which depends only on the non linear susceptibility of the molecules and an other part that characterizes the experimental setup. As a consequence, the bandshifts and widths of the SFG and infrared (IR) signals can be directly compared. Within the accuracy of the vibrational dependence of the molecular parameters, our calculations predict that the SFG signals connected to the symmetric vibrational modes should be more intense than the antisymmetric ones, in consistency with the IR and Raman spectroscopies and that the two symmetric modes should be observable while only the bending vibration has a significant intensity in IR. Finally, we discuss in terms of beam polarizations, the geometry of the experimental setup which optimizes the detected intensities.