Abstract: An exact numerical method was explored forTimoshenko-beam harmonic response. In the space domain, element free method relative only with the node was used and governing equations are the equivalent weakform instead of differential form. The amendment variation principle wasused to meet displacement boundary conditions and a least squares method to getthe shape function. The shape function was taken into the equivalent of the weakpoints to get the second-order discrete equation. In the time domain,precise integration was used and Romberg integration was adopted forthe non-homogeneous term. Finally, two examples ofnumerical results were obtained for the harmonicresponse problem at two different boundary conditions.