In this study, we propose to use Generalized Lindley (GL) and Power Lindley (PL) distributions as an alternative to the Weibull distribution for modeling the wind speed data. In the application part of the study, we consider the actual wind speed data collected in hourly basis from the Bilecik, Bursa, Eskisehir and Sakarya sites, Turkey in 2009. These data sets are modeled by using GL and PL distributions. To compare their modeling performance with well known and widely used Weibull distribution, Weibull distribution is also included into the study. The results show that GL distribution provides the best fitting according to root mean square error (RMSE), coefficient of determination (R-2), maximum value of the likelihood function corresponding to the ML estimates of the parameters (lnL) and Akaike information criterion (AIC). It is also seen that PL distribution is preferable in terms of power density error (PDE) criterion.