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Failure of laminated glass units is characterized by the growth and propagation of interfaces that can arise in unpredictable location of the layers. The paper presents the application of a theoretical model suitable in predicting the fracture path across the layers of laminated glass units when subjected to a static transversal load. The model falls in the context of the Strong Discontinuities Approach (SDA). All the relevant equations of the model derive from a variational principle formulated in a general context, thus allowing also for nonlinear continua. The numerical implementation in the Finite Element Method is based on Elements with Embedded Discontinuities concept. Relevant applications to laminated glass beams are presented and the results are compared with other theories.