An industrial laminate, Phenolic CE, is shown to possess seismic anisotropy. This material is composed of laminated sheets of canvas fabric, with an approximately orthogonal weave of fibers, bonded with phenolic resin. It is currently being used in scaled physical modeling studies of anisotropic media at The University of Calgary. Ultrasonic transmission experiments using this material show a directional variation of compressional- and shear-wave velocities and distinct shear-wave birefringence, or splitting. Analysis of group-velocity measurements taken for specific directions of propagation through the material demonstrates that the observed anisotropy is characteristic of orthorhombic symmetry, i.e., that the material has three mutually orthogonal axes of two-fold symmetry. For P waves, the observed anisotropy in symmetry planes varies from 6.3 to 22.4 percent, while for S waves it is observed to vary from 3.5 to 9.6 percent.From the Kelvin-Christoffel equations, which yield phase velocities given a set of stiffness values, expressions are elaborated that yield the stiffnesses of a material given a specified set of group-velocity observations, at least three of which must be for off-symmetry directions.