One-dimensional equations of the statics and free vibration of a strip beam made of an anisotropic material of general form (oblique anisotropy) are derived. It is shown that neither the Kirchhoff-Love hypotheses nor the classical Timoshenko-Reissner hypotheses lead to well-posed one-dimensional equations. A variant of the generalized Timoshenko-Reissner model is proposed that permits one to satisfy the boundary conditions on the beam surface exactly and leads to an asymptotically correct one-dimensional model. The solutions of the one- and two-dimensional equations of the statics and free vibration problems are compared and the dispersion equation is analyzed.