Combining the linear transformation and the solution technique for the cubic equation, a general closed-form analytic solution for bulk waves in orthotropic anisotropic materials is obtained. This method is straightforward and general. Degenerated cases include transversely isotropic, cubic, and isotropic materials. Numerical computations are carried out on a fiber-reinforced composite plate modeled as a transversely isotropic media. The fibers are parallel to the top and bottom surfaces of the plate, and they are rotated counterclockwise around the plate normal through different angles. The two-dimensional slowness curves corresponding to different rotations are presented graphically. The wave propagation characteristics displayed in slowness surfaces for different fiber orientation are analyzed. Combining the linear transformation and the solution technique for the cubic equation, a general closed-form analytic solution for bulk waves in orthotropic anisotropic materials is obtained. This method is straightforward and general. Degenerated cases include transversely isotropic, cubic, and isotropic materials. Numerical computations are carried out on a fiber-reinforced composite plate modeled as a transversely isotropic media. The fibers are parallel to the top and bottom surfaces of the plate, and they are rotated counterclockwise around the plate normal through different angles. The two-dimensional slowness curves corresponding to different rotations are presented graphically. The wave propagation characteristics displayed in slowness surfaces for different fiber orientation are analyzed.