Elastography is a method that can be used to measure the elasticity of soft biological tissue and, ultimately, to detect cancerous tumors. In this paper, quantitative elastography is developed using a fast multi-scale approach. Results are presented in simulation and preliminary results are presented in experiment. The optimization methods of elastography are applied to measure noninvasively the arterial wall stiffness of a vessel as well as blood pressure. Simulation results are presented that confirm the accuracy of methods, and preliminary experimental results are presented that measure pressure within a cylindrical cavity in a phantom. Using ultrasound, these methods could provide noninvasive continuous measurement of blood pressure in major arteries and could give doctors another method with which to gather information about a patient's cardiovascular health.