The paper deals with the problem of converting a continuous-time uncertain linear to an equivalent discrete-time uncertain and its digital simulation. The system matrices characterising the state-space representation of the original uncertain system are assumed to be interval matrices. The geometric series method together with interval arithmetic is employed to obtain the approximate discrete-time interval models. A new technique is developed to estimate the modelling errors. These modelling errors are used to modify the approximate interval models obtained via the interval geometric-series method. The resulting interval models (the enclosing interval models) are able to tightly enclose the exact uncertain model. Also their approximate discrete-time interval solutins are able to tightly enclose the exact interval solution of the continuous-time uncertain state-space equation. The proposed digital uncertain models can be used for digital simulation and digital design of continuous-time uncertain systems.