Vibrations of a thin elastic beam-strip are studied. A beam is made of an anisotropic material heterogeneous in the thickness direction. The 1D model of second-order accuracy is delivered by using asymptotic expansions in powers of the relative beam thickness. A special attention is paid to the slanted anisotropy with 6 elastic modules. A spectrum of bending vibrations in the case of simply supported ends of a beam is constructed. Forced vibrations under action of a harmonic and a random excitations are studied. In the last case, the root-mean-square of deflections are found in dependence of a type of excitation.