In order to investigate the effect of the opening rate and the vein angles on the unfolding manner of corrugated tree leaves, five paper models with various vein angles were considered. By using vector analysis, a series of numerical simulations for the unfolding of corrugated tree leaves was carried out. The midrib extension of Monarch birch leaves was also measured as an example of corrugated tree leaves. It was found that the extension rate of midrib is very small at an initial stage of unfdlding and then it becomes almost constant. From the simulation, it was obtained that the unfolding of leaves with constant kinetic energy makes the total kinetic energy minimum and gives a similar midrib extension pattern to the pattern of a real Monarch birch leaf.