This work discusses challenges we have encountered in acquiring reproducible measurements of shear wave speed (SWS) in the median nerve and suggests methods for improving reproducibility. First, procedural acquisition challenges are described, including nerve echogenicity, transducer pressure and transmit focal depth. Second, we present an iterative, radon sum–based algorithm that was developed specifically for measuring the SWS in median nerves. SWSs were measured using single track location shear wave elasticity imaging (SWEI) in the median nerves of six healthy volunteers and six patients diagnosed with carpal tunnel syndrome. Unsuccessful measurements were associated with several challenges including reverberation artifacts, low signal-to-noise ratio and temporal window limitations for tracking the velocity wave. To address these challenges, an iterative convergence algorithm was implemented to identify an appropriate temporal processing window that removed the reverberation artifacts while preserving shear wave signals. Algorithmically, it was important to consider the lateral regression kernel size and position and the temporal window. Procedurally, both nerve echogenicity and transducer compression were determined to impact the measured SWS. Shear waves were successfully measured in the median nerve proximal to the carpal tunnel, but SWEI measurements were significantly compromised within the carpal tunnel itself. The velocity-based SWSs were statistically significantly higher than the displacement SWSs (p < 0.0001), demonstrating for the first time dispersion in the median nerve in vivo using SWEI.