Abstarct: In this research,Dynamic response of an elastic thick cylindrical shell under moving load has been evaluated. The displacement field has been considered baxsed on the First order shear deformation theory and the motion equations have been derived using the Hamilton principle.These equations have been discritized with Galerkin weighted residual method. In addition by using the numerical centeral difference predictor ,the displacement has been calculated.A numerical code through the maple software has been prepared to calculate the displacements.The results of this code have been compared with the results obtained from Abaquse software .The conformity of the results show the validity of the used procedure.