The SPLASH experiment has been designed in 1985 by the CEA to simulate thermal fatigue due to short cooling shocks on steel specimens and is similar to the device reported by Marsh in Ref. [1]. The purpose of this paper is to discuss the mechanical and the fatigue analysis of the experiment using results from FEM computations. The lifetime predictions are obtained using a modified dissipated energy with a maximal pressure term and agree with the experimental observations. The numerical analysis of the mechanical state shows an important evolution of the triaxiality ratio during the loading cycle. Further comparisons and discussions of the fatigue criteria are provided in the second part of the paper (Part II).