Using composite cylinders assembly (CCA)model, a generalized algorithm has been developed to evaluate the micro stresses developed in the constituent phases of multiply (N-phases)coated hollow/solid fiber reinforced polymer matrix composites (PMCs)under different hygrothermal loading conditions. In the formulation all the N-phases are considered to be transversely isotropic. Results have been presented for S-glass/epoxy and AS-graphite/epoxy composites treating them as a five-phase (fiber, coating, matrix, and the composite)composite, void being the fifth phase along the centre line of the fiber. Results reveal the differences in the nature and the magnitude of stresses developed when solid fibers are replaced by the hollow ones. The algorithm can be utilized for evaluating the stresses in the constituent phases of multiply coated fiber reinforced metal matrix composites also where more than one coating layer and reaction zones, each with different constituent properties, are to be considered and the composite has to be treated as multiphase composite.