  We give a complete classification of the irreducible quasifinite modules for
algebras of the form Vir \otimes A, where Vir is the Virasoro algebra and A is
a Noetherian commutative associative unital algebra over the complex numbers.
It is shown that all such modules are tensor products of generalized evaluation
modules. We also give an explicit sufficient condition for a Verma module of
Vir \otimes A to be reducible. In the case that A is an infinite-dimensional
integral domain, this condition is also necessary.
