Environmental barrier coatings (EBCs) are proposed as an option to reduce the high temperature water vapour corrosion in gas turbines ceramic components made of Si3N4 or SiC/SiCf, which are projected to achieve further energy efficient gas turbines. These coating are commonly designed as multilayer systems firmly attached to the ceramic substrate with the aim of retarding or avoiding its degradation after exposure to environmental conditions close to those in gas turbines. Therefore, to fulfil this function crack formation/propagation in the coatings must be controlled. In present work, three types of environmental barrier coatings fabricated by air plasma spray and containing a Si layer attached to SiC substrate plus 2 to 5 layers of different mullite/Y2O3 stabilized–ZrO2 mixtures are examined. To determine the level of residual stresses in the as-sprayed coating/substrate systems a three dimensional finite element model is developed and also tested for same coatings but aged under, high temperature and rich water vapour atmosphere. The model calculates the zones of maximum tensile stresses in the coatings which agree with experimental observation identifying the type, number and location of cracks. This model could be extended to similar EBC systems, and more importantly, could be use as a powerful designing tool for these complex structures.