We review the principles of MR and ultrasonic approaches proposed for imaging the mechanical attributes or properties of tissues. We identify two groups of methods. One group of methods is based on the use of applied vibration to obtain information about tissue mechanical properties. The second group of methods is based on the application of quasi-static compression as a stimulus to map distribution of tissue mechanical attributes. Appropriate theoretical models are presented to explain both groups of methods. Finally, the principles of elastography are detailed with emphasis on its potential clinical applications.