Concrete and consolidated granular media in general exhibit a strong nonlinear hysteretic elastic behavior when excited by ultrasonic wave perturbations. Due to the sensitivity of their elastic properties to the small changes that can appear in their microstructure, the dynamic stress-strain relationship considered at low strains is affected by the presence of microcracks and hence the progression of damage. Tracking the nonlinear behavior can be made through the dependence on the excitation amplitude of the amplitude of higher order harmonics or of the resonance frequency of the sample. The present chapter shows a time domain analysis of elastic nonlinearity based on the break of the superposition principle when ultrasonic continuous waves are propagating in concrete samples. The latter, which can be of different microstructures (grain sizes, mortar, or polymer matrix), helps to understand the physical mechanisms involved in the different nonlinear elastic responses.