We are interested in Weil representations of Sp(2n, R), where R is the ring Z/plZ, p is an odd prime and l is a positive integer, or, more generally, R = [Oscr ]/[pfr ]l, where [Oscr ] is the ring of integers of a local field, [pfr ] is the maximal ideal of [Oscr ] and [Oscr ]/[pfr ] has odd characteristic. One reason for this interest is that a continuous finite-dimensional complex representation of Sp(2n, [Oscr ]) has to factor through a representation of Sp(2n, [Oscr ]/[pfr ]l) for some l.