This article focuses on the public stock buyback tender offers carried out in France between 1996 and 2005. First, we will study the impact of The Public Stock Buyback Tender Offers' announcements on stock prices. The results of the event studies show that these announcements are welcomed by a very favorable price reaction. Secondly, we try to explain the premium in the repurchase mode. The results of the linear regressions show that a low level of liquidity and the securities' performance, during the period preceding the public stock buyback tender offer, seems to push companies to pay large premiums. It also appears from these regressions that smaller companies, accepting the over demand and for a significant percentage from the capital; are also encouraged to offer high premiums.