The nonlinear propagation of elastic waves in soft solids, such as gelatin or brain, can easily give rise to shocks. Previous experimental and theoretical studies have described planar, focused, one dimensional, two dimensional polarized shear wave propagation in these media, as well as acoustic non linear propagation in wave guides. Here we present the behavior of guided shear waves in solid plates. A model based on a quasi-modal wave decomposition is described as well as a Fourier-based numerical solution that takes into account nonlinear, attenuating, dispersive, guided propagation. A mixed conventional time-space and Fourier domain numerical method is used to determine harmonic generation with propagation. These numerical solutions are validated by a comparison with experimental data for plane waves in gelatin and brain. It is then shown how the nonlinearity and dispersion due to the guiding geometry can act together to assist the formation of shocks. The model also predicts, similarly to fiber optics physics, that nonlinearity can give rise to a self phase modulation, which under specific conditions can be compensated by the dispersion resulting from the waveguide. It is shown that the model therefore predicts the existence of solitons -both theoretically and numerically.