A novel method for estimating the shear wave speed from crawling waves based on the amplitude modulation–frequency modulation model is proposed. Our method consists of a two-step approach for estimating the stiffness parameter at the central region of the material of interest. First, narrowband signals are isolated in the time dimension to recover the locally strongest component and to reject distortions from the ultrasound data. Then, the shear wave speed is computed by the dominant component analysis approach and its spatial instantaneous frequency is estimated by the discrete quasi-eigenfunction approximations method. Experimental results on phantoms with different compositions and operating frequencies show coherent speed estimations and accurate inclusion locations.