This article summarizes the theory and demonstrates the technique of a new scaling method known as the Lie scaling. In the course of applying the method to two example problems, classical notions of dynamical and kinematic scaling are incorporated. The two example problems are a 2-D unconfined groundwater problem in a heterogeneous soil and a 1-D contaminant transport problem. The article concludes with comments on the relative strengths and weaknesses of Lie scaling and classical scaling.