Composite materials exhibit various and complex failure behavior. Diff
erent formalisms have been used to predict failure. Improvement of old
theories and new ones continue to be published. In this paper, the mo
st recent and widely used models are presented. Failure criteria such
as Tsai-Wu, parametric formulations, maximal stress and strain, Hashin
criterion, Hart-Smith criterion, and the method based on kriging are
presented. These failure theories may be classified in two categories,
depending whether they integrate failure modes or not. The formalism
of each theory is briefly described and their application to model fai
lure of composite laminates is discussed by comparing the advantages a
nd limitations of each method. The diversity of experimental failure e
nvelopes, as reported in the literature on composites, is outlined and
it is shown that most criteria permit modeling only particular failur
e properties of composite laminates.