For centuries tissue palpation has been an important diagnostic tool. During palpation, tumors are felt as tissues harder than the surrounding tissues. The significance of palpation is related to the relationship between mechanical properties of different tissue lesions. The assessment of tissue stiffness through palpation is based on the fact that mechanical properties of tissues are changing as a result of various diseases. A higher tissue stiffness translates into a higher elasticity modulus. In the 90's, ultrasonography was extended by the option of examining the stiffness of tissue by estimating the difference in backscattering of ultrasound in compressed and non-compressed tissue. This modality is referred to as the static, compression elastography and is based on tracking the deformation of tissue subjected to the slowly varying compression through the recording of the backscattered echoes. The displacement is estimated using the methods of cross-correlation between consecutive ultrasonic lines of examined tissue, so calculating the degree of similarity of ultrasonic echoes acquired from tissue before and after the compression was applied. The next step in the development of ultrasound palpation was to apply the local remote tissue compression by using the acoustic radiation force generated through the special beam forming of the ultrasonic beam probing the tissue. The acoustic radiation force causes a slight deformation the tissue thereby forming a shear wave propagating in the tissue at different speeds dependent on the stiffness of the tissue. Shear wave elastography, carries great hopes in the field of quantitative imaging of tissue lesions. This article describes the physical basis of both elastographic methods: compression elastography and shear wave elastography.