An element of a group is called \emph{reversible} if it is conjugate to its inverse, and \emph{strongly reversible} if it can be expressed as a product of two involutions. We study strongly reversible elements in the Riordan group and in several of its important subgroups. We show that not every reversible element in the Riordan group is strongly reversible, and we investigate products of reversible elements in the Riordan group.