Stretching-driven swelling of polyrotaxane (PR) gels whose cross-linked cyclic molecules can slide along the network strands in response to imposed strain is investigated as functions of cross-link concentration (c(x)), the length of network strands (M-s) and the content of cyclic molecules threaded onto the network strands (phi(CD)). For the PR gels with high c(x), equilibrium Poisson's ratio (mu(infinity)) which is a measure of stretching-driven swelling is independent of imposed stretch (lambda) as in the case of classical gels with fixed cross-links. In contrast, mu(infinity) for the PR gels with sufficiently low c(x) depends on lambda: mu(infinity) increases with lambda in the regime of lambda < lambda(c) whereas mu(infinity) levels in the region of lambda > lambda(c). The lambda-dependent mu(infinity) under moderate elongation is attributed to a function characteristic of movable cross-links (pulley effect) which can vary the network topology under imposed deformation so that the configurational entropy can be maximized. The level-off behavior of mu(infinity) at high elongation is explained by the suppression of pulley effect caused by high stacking and/or localization of cross-linked cyclic molecules at the chain ends. The content phi(CD) influences the variation in the lambda dependence of mu(infinity) driven by a change in c(x) as well as the values of mu(infinity). These results indicate that (1) the cross-links in the PR gels move nonaffinely and (2) phi(CD) influences how the cross-links slide along the network strands in nonaffine manner in response to imposed deformation.