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Measurement of shear wave propagation speed has important clinical applications because it is related to tissue stiffness and health state. Shear waves can be generated in tissue by the radiation force of a focused ultrasound beam (push beam). Shear wave speed can be measured by tracking its propagation laterally from the push beam focus using the time-of-flight principle. This study shows that shear wave speed measurements with such methods can be transducer and depth dependent. Three homogeneous phantoms with different stiffness were studied using curvilinear and linear array transducer. Shear wave speed measurements were made at different depths and using different aperture sizes for push. The curvilinear transducer shows a relatively large measurement bias that is depth dependent. The possible causes of the bias and options for correction are discussed. These bias errors must be taken into account to provide accurate and precise time-of-flight based shear wave speed measurements for clinical use.