I need to use a variance buffer shadow sunlamp to illuminate a scene in the game engine yet I have not succeed in obtaining correct shadows from my alpha planes as you can see in this picture. Is it possible ?
Variance lights do not support alpha channel. I'm not sure why. Simple shadows do (as pointed out in one of the other answers), but as you have discovered, variance shadows do not.
To enhance the effect of a bigger shadow area, you can vertex-parent the sun to the player, so it follows them around. This way you can get a 512x512 shadow map to appear to cover the entire map.
Sorry I can't be of any further help.
If you are looking for what is in the image you have posted, then bumping up the sun value to 6000 gave me this:
Otherwise: my understanding of your intent, is that you wanted the shadows to match the shape of the Leaves, like the following image.
The biggest for me was to do two primary things:
Make sure that my Leaves had a true Alpha Channel (not just Black to Alpha)
Changing shadow type from Variance to Simple on the Sun Lamp.
Note In the viewport this does not work, but in game it works.
Here's the blend so you can cruise around and match any settings I messed with, just in case I missed something, plus I also packed my horrible version of a leaf texture image in here for you to make sure you have a visual reference to understand what I mean regarding the Alpha Channel.