Methods of modeling a transistor are provided. The method includes the steps of (a) extracting reference mobility values of a channel layer of a transistor including a gate electrode, a source region and a drain region using a reference gate voltage, a reference drain current and a reference drain voltage, (b) fitting a mobility function including model parameters on the reference mobility values to extract the model parameters, and (c) putting the extracted model parameters into a drain current modeling function to calculate a drain current flowing through the channel layer between the drain region and the source region under a bias condition defined by an arbitrary gate voltage applied to the gate electrode and an arbitrary drain voltage applied to the drain region. Related apparatuses are also provided.