It is the aim of the present work to address some of the aspects of microcracking in electron beam deposited scandia-stabilised zirconia electrolyte applied for solid oxide fuel cells (SOFC) where a thin electrolyte layer is deposited on a relatively thick anode substrate. A model of microcracking for the electrolyte material is proposed which takes into account the statistical distribution of grain sizes, the stress redistribution due to failure of individual structural elements as well as the local criterion of grain fracture. The combination of electron microscopy research with model calculations permits both the specific energy of new surface creation in the electrolyte and critical parameters of the microcracking process to be determined. The annealing-induced electrolyte microcracking discussed in this work corresponds to localised microcracking, where each next structural element fails mainly at an existing microcrack tip. The features of localised microcracking in electron beam deposited scandia-stabilised zirconia electrolyte are analysed.