We present here a quantitative study of dislocation cross-slip, an essential thermally activated process in deformation of metals, in discrete dislocation dynamics (DDD) simulations. We implemented a stress-dependent line-tension model in DDD simulations, with minimal information from molecular dynamics (MD) simulations. This model allows reproducing in DDD simulations the probabilistic cross-slip rate calculated in MD simulations for Cu in a large range of stresses and temperatures. This model opens new horizons in modelling cross-slip related mechanisms such as deformation softening, dislocation-precipitate interaction and dislocation patterning in realistic strain rates.