This study is intended to analyze free and forced vibrations of non-uniform composite beams in the Laplace domain. The free vibration is then taken into account as a special case of forced vibration. The Timoshenko beam theory is adopted in the derivation of the governing equation. The material of the rod is assumed to be homogeneous, linear elastic and anisotropic. The effects of shear deformation, rotary inertia, non-uniformity of the cross-section are considered in the formulation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem accurately. The effects of non-uniformity parameters and angle of fibre orientation on dynamic behaviour are investigated.