Use of wood-fiber plastics for construction purposes calls for comprehensive understanding of their anisotropic mechanical properties. As a respective contribution, we here report the first-ever complete elasticity characterization of an orthotropic bagasse fiber polypropylene composite, requiring identification of nine independent constants. For this purpose, we carry out characterization in principal material directions. Six diagonal stiffness tensor components are quantified based on ultrasonic longitudinal and shear wave velocity measurements; and three diagonal compliance tensor components are identified as the inverses of three Young’s moduli derived from unloading regimes of quasi-static uniaxial compression tests. Combination of all measurement data in the framework of orthotropic linear elasticity provides access to all off-diagonal stiffness and compliance tensor components, opening the door to quantifying six Poisson’s ratios.