The present study addresses the integration of an analytical uncertainty quantification approach to multi-scale modeling of single-walled carbon nanotube (SWNT)-epoxy nanocomposites. The main highlight is the investigation of the stochasticity of nanotube orientations, and its effects on the homogenized properties. Even though the properties of SWNT-epoxy nanocomposites are well-studied in the literature, the natural stochasticity that arises from the nanotube orientations has not been observed. To understand the effects of the variability in SWNT orientations to material properties of interest, an analytical uncertainty quantification algorithm is utilized. The analytical scheme computes the propagation of the orientational uncertainty to the volume-averaged properties with a linear solution and uses the transformation of random variables principle to obtain the variations in non-linear properties. The results indicate that the uncertainty propagation affects the macro-scale properties, including stiffness, thermal expansion, thermal conductivity, and natural frequencies.