In this thesis, the response of DNA and RNA to linear and torsional mechanical stress is studied using coarse-grained models. Inspired by single-molecule assays developed over the last two decades, the end-to-end extension, buckling and torque response behaviour of the stressed molecules is probed under conditions similar to experimentally used setups. Direct comparison with experimental data yields excellent agreement for many conditions. Results from coarse-grained simulations are also compared to the predictions of continuum models of linear polymer elasticity. A state diagram for supercoiled DNA as a function of twist and tension is determined. A novel confomational state of mechanically stressed DNA is proposed, consisting of a plectonemic structure with a denaturation bubble localized in its end-loop. The interconversion between this novel state and other, known structural motifs of supercoiled DNA is studied in detail. In particular, the influence of sequence properties on the novel state is investigated. Several possible implications for supercoiled DNA structures in vivo are discussed. Furthermore, the dynamical consequences of coupled denaturation and writhing are studied, and used to explain observations from recent single molecule experiments of DNA strand dynamics. Finally, the denaturation behaviour, topology and dynamics of short DNA minicircles is studies using coarse-grained simulations. Long-range interactions in the denaturation behaviour of the system are observed. These are induced by the topology of the system, and are consistent with results from recent molecular imaging studies. The results from coarse-grained simulations are related to modelling of the same system in all-atom simulations and a local denaturation model of DNA, yielding insight into the applicability of these different modelling approaches to study different processes in nucleic acids.