Laser Doppler Vibrometry (LDV) is a non-contact technique for sensing surface vibrations. Traditionally, LDV uses one or more fixed beams to measure the vibrational velocity of specific points and orientations. In order to measure an angular velocity at least two laser beams are required. Instead, this research proposes to develop a Continuous Scanning Laser Doppler Vibrometer (CSLDV) technique, based on a single laser beam continuously sweeping the area of interest using a scanning mirror. Linear scans allow the measurement of normal and angular velocity while circular scans allow the measurement of normal velocity and two angular velocities. The first part of the study analyzes the performance of rigid body models of both the short line and circular scans (< 1 cm) for measuring low broadband frequency vibrations of gel samples. This thesis focused on low frequency broadband vibration since natural human body vibrations (such as tremor or breathing) are typically below a few hundred hertz. Results for normal and angular velocity measurements are validated against conventional method of using two fixed LDVs. The second part of this research investigates the CSLDV technique for longer scans (< 5 cm). These long scans will be used to act as an array of virtual transducers at multiple points along the scanning path of the single laser beam; thus yielding similar information obtained using an array of several real fixed LDVs. A practical challenge encountered when using CSLDV is speckle noise, that is generated when a coherent light source is reflected back from an optically rough surface. The effect of speckle noise will be quantified by varying different parameters such as scan lengths, scanning frequency, target to sensor distance and the amplitude of excitation. These parameters will be optimized in order to reduce the error of vibration measurements obtained from the CSLDV. Such systems will be used to monitor multiple degrees of freedom of human skeletal muscle vibrations for elastography purposes. The forced vibration of human muscles will be analyzed using these CSLDV techniques. Overall contributions of this work include: (1) Validation of rigid body models of both short line and circular scans CSLDV for broadband low frequency linear and angular velocity measurements; (2) application to sensing natural human body vibrations (e.g., hand tremors); (3) replacement of an array of vibration sensors by a single long line scan CSLDV. (4) development of a dynamic elastography technique for skeletal muscles using CSLDV.