Models for the investigation of transients MHD flows are presented in this paper. Both the study of transients caused by the finite flow time of the plasma through the channel and by transitions between different operating conditions of the generator are considered. The analysisof physical phenomena as plasma relaxation and non-uniformities belong to the first case. Transients originated by changes of the operating conditions and faults are of the second case. In order to perform the mentioned study, one-dimensional and two-dimensional time dependent models have been set up. The models are presented in this note. The analysis of the transient during the start up of a linear gas fired generator is shown.