This research explores factor analysis applied to data from skewed distributions for the general skew model, the selection-elliptical model, the selection-normal model, the skew-elliptical model and the skew-normal model for finite sample sizes. In terms of asymptotics, or large sample sizes, quasi-maximum likelihood methods are broached numerically. The skewed models are formed using selection distribution theory, which is based on Rao’s weighted distribution theory. The models assume the observed variable of the factor model is from a skewed distribution by defining the distribution of the unobserved common factors skewed and the unobserved unique factors symmetric. Numerical examples are provided using maximum likelihood selection skew-normal factor analysis. The numerical examples, such as maximum likelihood parameter estimation with the resolution of the “sign switching” problem and model fitting using likelihood methods, illustrate that the selection skew-normal factor analysis model better fits skew-normal data than does the normal factor analysis model.