This study proposes the use of Gaussian mixture models to represent non-Gaussian correlated input variables, such as wind power output or aggregated load demands in the probabilistic load flow problem. The algorithm calculates the marginal distribution of any bus voltage or power flow as a sum of Gaussian components obtained from multiple weighted least square runs. The number of trials depends on the number of Gaussian components used to model each input random variable. Monte Carlo simulations are used to compare the approximations. The effect of correlation between variables is taken into consideration in both formulations. The main advantage of the Gaussian components method is that the probability density functions of any variable is directly obtained. Test results in the 14-bus system and the 57-bus system provide a broad explanation of the advantages and constraints of the approximations, particularly in presence of correlated variables.