  We introduce the notion of algebraic volume density property for affine
algebraic manifolds and prove some important basic facts about it, in
particular that it implies the volume density property. The main results of the
paper are producing two big classes of examples of Stein manifolds with volume
density property. One class consists of certain affine modifications of $\C^n$
equipped with a canonical volume form, the other is the class of all Linear
Algebraic Groups equipped with the left invariant volume form.
