Abstract
The aims of this paper are to study the modality of skew t-distribution and the mixture of skew t-distributions graphically and analytically. We introduced a new formula to find the modes for univariate skew t-distribution and the mixture of univariate skew t-distribution. We also explored the effect of the skewness parameters and the degrees of freedom on the number and locations of modes for univariate skew t-distribution and in the mixture of skew t-distribution. Exploring the modes for the mixture of skew t-distribution helps the research to discover when and which components of the mixture can be merged in one homogeneous group to get the best results when exploring the data set.