In the previous paper, the authors presented analytical formulae for the elastic moduli of unidirectional fiber-reinforced composite materials. In these expressions, an empirical coefficient such as contiguity factor has been used, which is similar with one proposed by Tsai, but is assumed to be a linear function of fiber volume fraction. In the present paper, refining the previous research, the analytical formulae are first proposed by considering the square array of reinforced fibers without introducing an empirical factor used in the previous paper. Comparing with the proposed formulae by other authors, these analytical values agree well with the experimental results on glassfiber/epoxy composites which are obtained by the authors. In addition, the analytical formulae for elastic moduli of multilayered composite, that is, the helical-wound cylinder or the alternating helical and circumferential winding cylinder such as applied to rocket chamber, are proposed by using the elastic moduli of unidirectional fiber-reinforced materials proposed firstly in the present paper. These analytical values show a good agreement with the experimental values on filament-wound cylinders of various sorts of winding angle which are obtained by the authors.