The crack tip (mode I, mode I + II) stress singularities in orthotropic composites are studied by the method of reflective caustic. Based on the caustic parametric equations and its initial curves surrounding the crack tip derived by the elastic crack solutions of composites and the principle of reflective caustic, theoretical caustics and initial curves at mode I and mixed mode (I + II) crack tip of fibre orthotropic composites are simulated. Influences of material orientation on crack tip singularities in composites are analysed. The static experimental caustics of mode I and mixed mode I + II crack tip in composites are obtained when the initial crack direction is parallel to the main axis of the orthotropic material, i.e. θ = 0°. The results indicate that the experimental caustics obtained from the actual fibre composites have a remarkable difference compared with the simulation caustics based on the fracture theory of continuum orthotropic composites, which provide an important physical foundation for understanding the singular stress characterizations at the crack tip of composite materials.