Long EHV transmission lines are generally compensated by means of shunt reactor sets. Reactor failures have directed attention to the transient overvoltages generated by reactor switching. 750 kV site measurements have shown that arrester operations or breaker restrikes could cause particularly dangerous steep reactor voltages. The paper introduces a comprehensive EMTP-type model of the reactor and the surrounding system (busbar, breaker, arrester, transformer, supply side network). The computer model has been tested by field experiments. A similar computer model has been elaborated for the study of transients, caused by de-energising reactors connected with the 18 kV tertiary winding of the 420/132 kV autotransformers. The model has been validated using a pushing into service test of a new air core shunt reactor, equipped with SF 6 circuit breakers. The computer models are easy to use for case studies, as well as in simulations to predict those variables which were not, or can not, be measured in the field tests. This paper introduces elements of the elaborated EMTP model, some steps of the model testing and verification. This paper contains the results of the computer analysis and of the field experiments.