A composite model with periodic distributed reinforcement is adopted to study the elastic behaviour of multiply coated fiber composites under antiplane shear forces. Referring to the concept of eigenstrain and using the theory for doubly quasi-periodic Riemann boundary value problems, the problem of periodic distributed inclusions is transformed into that of homogeneous materials with periodic distributed eigenstrains. The elastic fields in the fibers, coatings and matrix are obtained in series form. Several comparisons with the finite element method, generalized self-consistent method and asymptotic homogenization method are made to demonstrate the accuracy of the present method. The influences of the thickness and stiffness of coatings on interfacial stress concentration and effective longitudinal shear modulus are discussed. The present method provides an efficient tool for interfacial effect analysis of multiply coated fiber composites.