Soft biological tissue elasticity is a parameter whose reliable measure is relevant to many applications in fields as diverse as medicine and the agrifood industry. The ultrasonic elastography methods are often unviable to be applied to provide such solutions. In this way, the surface wave elastography (SWE) appears as a viable alternative, due its low cost, easy to use, non-invasive-destructive character as well as its ability to provide in vivo estimates. Previous studies have described a good correlation between the overall behavior of ultrasonic elastography and SWE, although the latter overestimates the elasticity values compared to the first. It has been suggested that this is due to the influence of certain physical effects related to the exclusive use of low frequency waves, as well as by characteristics of the experimental setup and/or medium. In this work we confirm the influence of such effects and discuss different strategies to make independent the estimations thereof. This allows achieving a good agreement between the ultrasonic reference method and SWE. Thus, SWE becomes a reliable method to estimate soft biological tissue elasticity.