The progressive failure process in composites involves many types of damage initiating and propagating in a strongly coupled fashion. The various damage modes typically include ply cracking, delamination, fiber rupture (in tension), and kink band formation (in compression), etc. Recent developments in advanced numerical methods such as X-FEM and A-FEM have been able to treat such coupled damage evolutions, provided appropriate crack initiation and propagation criteria are available. Currently strength criteria calibrated from individual damage modes are being used. However, recent multiscale composite simulations and high-resolution material characterizations have shown that the crack initiation is significantly influenced by local material heterogeneity at single fiber scale (∼ 5- 10 microns). The empirical based initiation criteria cannot reflect such reality and needs further improvement. In this paper, we shall seek a method that has the potential to yield high fidelity damage initiation prediction with explicit consideration of local material heterogeneity. The approach employs weight-function method to analyze the microscopic failure with a domain that contains large enough number of randomly distributed fibers. Concentrated local stresses due to local material heterogeneity and cracking are computed through a generic 3-fiber interaction problem with varying local material heterogeneity. The results will then be applied to the entire domain using weight function method. The method needs not to solve the inverse problem with large degree of freedoms. Therefore the microscopic analysis will be very fast and efficient.