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We propose a new light on the dispersion of Li in the atmosphere of solar type stars, based on a set of 56 solar analogs among them 20 solar twins, by comparing to new stellar evolution calculations (models STAREVOL). Stellar spectra from the ELODIE spectrograph attached at the 1.93 m telescope in Haute-Provence Observatoire (France) were used. Lithium abundances were derived by comparing observed and synthetic spectra in the region of Li I line 6707 , taking into account NLTE corrections. We discuss the observed scatter in Li abundance of solar twins as a function of age, rotation velocity vsini , and other factors. We compare to the predictions of stellar evolution models which include different transport processes for angular momentum and chemicals.