In spite of their advantages, e.g. high strength, low weight, and high stiffness, composite laminates are prone to the formation of transverse cracking during both manufacture and service. It has been well recognised that the core to this damage mode is stress singularities near transverse cracks. In addition, transverse cracking may cause degradation in the thermoelastic properties of a laminate, and meanwhile new ply cracks usually form with the increase of applied loading. As a result, the stress transfer near transverse cracks, thermoelastic property degradation due to transverse cracking, and propagation of transverse cracks are all important issues in the analysis of composite laminates. The major contribution of this work is to develop a new semi-analytical method, the state space method, to evaluate the stress transfer near free edges and transverse cracks. On the basis of the generalised plane strain condition, the method overcomes the limitation of analytical methods in study nonsymmetric laminates. Moreover the method guarantees continuous fields of interlaminar stresses across interfaces between layers, which is one of the obstacles for conventional finite element method. Another contribution is to apply the stress analysis to assess the thermoelastic property degradation induced by transverse cracAking in general cross-ply and symmetric angle-ply laminates. The prediction is made by using the constitutive equation of laminates in the Classical Laminate Theory. The numerical results of stiffness degradation for nonsymmetric cross-ply laminates are revealed for the first time in the literature. The final contribution of this work is to apply the stress analysis to predict propagation of transverse cracking in general composite laminates. An energy-based cracking criterion is used to predict the crack multiplication process. The predictions for nonsymmetric laminates and the effects of shearing to transverse cracking are believed to be the first solutions in the literature.