Expressions and bounds for the five effective elastic moduli of a unidirectional fiber composite, consisting of transversely isotropic fibers and matrix, are derived on the basis of analogies between isotropic and transversely isotropic elasticity equations. Application of results for determination of the five elastic moduli of graphite fibers is discussed. Effective thermal expansion coefficients are derived on the basis of a general theorem. Effective conductivities, dielectric constants, and magnetic permeabilities are derived by use of certain mathematical analogies.