We investigate the potential of Brillouin Light Scattering (BLS) Microspectroscopy for fast non-invasive all-optical assessment of the mechanical properties of viscose fibers and bleached softwood pulp. Using an optimized Brillouin spectrometer, we demonstrate fast spatial mapping of the complex longitudinal modulus over extended areas (> 100 mu m). Our results reveal that while the softwood pulp has a relatively uniform moduli, the viscous fibers have significant spatial heterogeneous in the moduli. Specifically, the viscose fibers exhibited a regular pattern of increasing and decreasing modulus normal to the fiber axis. The potential influence of a locally changing refractive index is investigated by holographic phase microscopy and ruled out. We discuss our results in light of the anisotropic mechanical properties of the fibers and are able to estimate the relative difference between the modulus along the fiber axis and that perpendicular to it. Results are presented alongside reference measurements of the quasi-static mechanical properties transverse to the fiber axes obtained using AFM-nanoindentation which reveal a similar trend, hinting at the potential usefulness of BLS for mechanical characterization applications. However, more detailed investigations are called for to uncover all the factors influencing the measured high-frequency BLS modulus and its significance in relation to physical properties of the fiber that may be of practical interest.