The objective of this paper is to introduce a novel fast modeling tool called peri-ultrasound for linear/nonlinear ultrasonic wave propagation modeling. This modeling approach is based on peridynamic theory. It does not require monitoring of the crack clapping phenomenon or artificially changing the stiffness of the element when two surfaces of the crack come in contact. Peri-ultrasound tool enables us to detect the material nonlinearity in very early stages of crack growth. Nonlinear ultrasonic behavior could be nicely modeled by the proposed peri-ultrasound tool. It is investigated how the material nonlinearity is affected by the presence of thin and thick cracks. From the normalized spectral plots the degree of material nonlinearity can be measured by extracting a feature called sideband peak count (SPC). Structures containing a thin crack show noticeable increase in their nonlinear behavior.