Guided wave mixing leverages mutual wave interactions to provide sensitive diagnostics of material degradation in plates and pipes and an early warning upon which maintenance decisions can be based. In some cases, the material to be interrogated may be otherwise inaccessible for nondestructive evaluation. The distortion of the waveform in nonlinear ultrasonics is typically quite small, often making it difficult to distinguish from nonlinearities in the sensing system. Mutual wave interactions are preferred to wave self-interactions in this respect because they can be designed to occur away from frequencies corrupted by sensing system nonlinearity. Furthermore, primary waves that generate secondary waves having a different polarity also provide a means to separate the material nonlinearity from the sensing system nonlinearity. Finite element simulations of wave mixing using a hyperelastic material model are conducted as a precursor to laboratory experiments to establish realistic expectations. In one case, shear-horizontal waves are mixed with co-directional symmetric Lamb waves to generate backpropagating shear-horizontal waves at the difference frequency. In the second case, counterpropagating shear-horizontal waves mix to generate secondary standing waves at the cutoff frequency of the S1 Lamb wave mode. In both cases, the results indicate that the larger the wave mixing zone, the more measurable is the amplitude of the secondary waves. These results will be used to design experiments that demonstrate the utility of these novel wave interactions.