In this paper the dynamic behavior of a viscoelastic beam subjected to a moving distributed load has been studied analytically. The viscoelastic properties of the beam have been considered as the linear standard model in shear and incompressible in bulk. The stress components have been separated to the shear and dilatation components then, the governing equation in viscoelastic form has been obtained with direct method and it has been solved with the eigenfunction expansion method. Using the obtained dimensionless coefficients from the governing equation, an analytical procedure has been presented and by parametric studies the effects of the load properties and viscoelastic materials on the amplitude and frequency of the response have been investigated. Such results can present an idea for selecting some parameters in engineering design.