For some of the applications of the Second-order UltRasound Field (SURF) imaging technique, a real-time delay-estimation algorithm has been developed for estimating spatially range-varying delays in RF signals. This algorithm is a phase-based approach for subsample delay estimation, and makes no assumption on the local delay variation. Any parametric model can be used for modeling the local delay variation. The phase-based delay estimator uses estimates of the instantaneous frequency and the phase difference and the relationship between the two to estimate the delay. The estimated delay may be used to calculate an improved estimate of the instantaneous frequency, which in turn may be used to calculate new, updated values for the delay using an iterative scheme. Although an iterative scheme introduces a larger bias, the estimated delay values have a significantly lowered standard deviation in comparison to the original method. The delay estimator originally developed for estimating propagation delays for SURF imaging, can also be used for elastography purposes. By not being restricted to locally constant delays, the delay estimator is able to more robustly estimate sharp changes in tissue stiffness, and in estimating small differences in strain more closely. Two different parametric models for the local delay have been tried, one linear, and one polynomial of the first degree. The two various models have been tested on an elastography recording provided by the Ultrasonix company (Ultrasonix Medical Corporation, Vancouver, Canada), and in vitro. Using a polynomial of the second degree as parametric model for the delay is better than a linear model in detecting edges of inclusions located at a depth where the strain is lower than closer to the transducer surface. The differences may be further emphasized by performing spatial filtering with a median filter. The downside of updating the model is an increased computational time of approximately 50%. Multiple reflections, also known as reverberations, appear as acoustic noise in ultrasound images and may greatly impair time-delay estimation, particularly in elastography. Today reverberation suppression is achieved by second harmonic imaging, but this method has the disadvantage of low penetration, and little or no signal in the near field. The SURF imaging technique has the advantages of reverberation suppression in addition to imaging in the fundamental frequency. A reverberation model has been established, and the effect reverberations have on estimated elastography images is studied. When using a layered silicon plate as reverberation model, and imaging through this initial reverberation model placed on top of the imaging phantom, elastography images were not obtained as the quality of the recording was degraded as a result of power loss. By adding reverberations by computer simulations after a recording with a SURF probe with reverberation suppression was performed, a markedly difference between elastography estimates done on the image with reverberations, and the image with reverberations and reverberation suppression was observed. Estimating on a signal with reverberations, the phase-based time-delay algorithm was unable to distinguish any differences in elasticity at all. Estimating time delays on a signal with reverberations and SURF reverberation suppression however, the algorithm was able to clearly estimate differences in strain, and display the presence of an inclusion.