Knowledge of the shear elasticity of soft tissues is relevant in many areas of medicine since some diseases correlate with changes in elasticity. Therefore, over the past 30 years, various noninvasive methods have been developed to estimate tissue elasticity. These methods are generally known as elastography. Most of them are ultrasound-based methods requiring specially adapted ultrasound scanners in order to quantify the elasticity. Elastography has the potential to add value and knowledge to other research areas like biomechanics, sports medicine or even the meat and/or agrifood industries. However, the existing solutions are not well adapted to those applications. Hence the need for a portable and reliable elastography method. In this work, we present a nonultrasound surface wave elastography device and method to estimate the shear elasticity of soft tissues. The method is based on surface wave propagation. Inversion algorithms were developed to retrieve the shear elasticity from the surface wave phase velocity in isotropic and transversely isotropic solids. The algorithms take into account near-field effects usually neglected in surface wave elastography. A detailed description of the device is given. The method was tested in tissue-mimicking phantoms and in beef samples. In addition, in vivo applications to estimate the biceps elasticity of two volunteers are shown. The obtained results are comparable to those obtained by other methods, such as shear wave elastography.