Based on the angio elastography principle, the variation in blood-vessel diameter with pressure is measured by the photoacoustic elastography technique. A characteristic time-domain model for photoacoustic signals is developed to analyze the information of the blood pressure-diameter relation. A series of digital signal-processing methods based on the Hilbert transform are used to obtain spatial distributions of elastic mechanical properties in tissues. Results demonstrate that the pressure and vessel diameter have a monotonously increasing relation with the photoacoustic-signal time interval, which can be used to dynamically and quickly detect changes in the vessel diameter. This method provides a theoretical basis for non-invasive ambulatory blood-pressure measurements by photoacoustic imaging.