A geometric averaging is employed in a scale transition model dedicated to determining the effective hygro-elastic macroscopic properties of a fiber-reinforced composites from the properties of its constituents (i.e., the fiber and the matrix), for the first time. Calculations of macroscopic and local stresses due to hygroscopic loads are also carried out. Numerical computations performed according to the geometric mean are compared to the corresponding predictions given by the arithmetic average, classically used in the field of micro-mechanical modeling.