In general, the use of fibers requires sorting and, in some cases, chemical treatments, which increases the manufacturing cost and environmental impact. The use of short, unorganized fibers, i.e., randomly distributed, is a solution to this problem. However, to use randomly distributed short natural fibers, the mechanical properties of the randomly reinforced composite must be estimated. This paper developed two analytical models and one finite element model to characterize composites reinforced with short fibers. Calcium Carbonate precipitates CCP/PVC PolyVinyl Chloride composites are studied as an application in the construction industry. The CCP improves recyclability and reduces petrochemical and energy usage during the manufacturing process, minimizing the carbon footprint. The Mori-Tanaka model, the Halpin-Tsai model, and a finite element method model were used to investigate distribution effects on the mechanical properties of the composite. The first is the effect of fiber volume fraction on the elastic mechanical properties of the composite. All three models show an increase in elastic modulus with the growth of fiber content in the composite. The second is the effect of fiber orientation for a given volume fraction. The results show a maximum variation of 15.56% on the elastic properties by varying the fiber orientation compared to an equally distributed composite. This result means that the random distribution of the fibers does not significantly influence the mechanical properties. The third effect is the fiber length effect. For different concentrations, the fiber length varies the stiffness by about 6.64%. This variation of the stiffness is observed up to the ratio of fiber length/diameter equal to 100; after that, the increase is insignificant.