This presentation discusses modeling the propagation of nonlinear waves in a continuum phononic material. This system is shown to exhibit amplitude-dependent response and energy transfer between frequencies, which are well studied phenomena of nonlinear discrete systems, but are relatively unexplored in fully elastic continuum models. The phononic material is composed of repeated layers of stiff and soft materials, and the nonlinearity is introduced through a nonlinear hyperelastic Gent model in the soft material. We analyze the dispersion of the linearized system using Bloch-wave analysis to identify band gaps in the system, and we use full-scale time-domainfinite element simulations to analyze the dynamic behavior of the system. Generation of zero frequency and second harmonic frequency amplitudes as well as their accumulation with distance are observed, and the influence of phononic band gaps on nonlinear wave propagation are described. We explore the influence of material nonlinearity in soft materials in continuum phononic materials as a mechanism for control of nonlinear wave propagation.