The use of extruded insulation for DC cables involves a risk of local electric field enhancement, caused by a space charge build-up within the dielectric. In this work, the theory of charge generation and transport in polymers is applied in a numerical computer model in order to predict the formation and transport of space charges in a polymeric dielectric. The model incorporates the processes of field assisted electron-hole pair generation from impurity atoms, trapping and charge injection at the electrodes. Its aim has been to study the field- and temperature dependent dynamic behaviour of a dielectric. Results obtained using this model-based framework are compared to measurement results obtained from Laser Induced Pressure Pulse (LIPP) space charge measurements as well as conductivity measurements on selected cable type samples.