Low-density fibrous composites are composed of fibers, binder, and air, and exhibit mechanical properties that strongly depend upon the characteristics of the individual constituents. Three dimensional models are developed to predict the effective stiffness and strength of this type of composites. The predicted computational mechanical properties are compared to experimental values obtained for a glass-fiber composite with excellent agreement. Monte Carlo simulations were then performed to study the dependence of the composite effective stiffness on fiber diameter, length, orientation and mechanical properties. Results indicate that for a specific type of fiber and volume fraction, fiber orientation is the parameter determining the behavior of the composite effective stiffness.