By the analysis of force-balance of cylinder element,the differential equation of viscoelastic cylinder is derived based on the D Alembert,s principle.And the operators of Kelvin model solid model are introduced into the differential equation respectively,and then the differential equations of viscoelastic cylinder with Kelvin model solid model are established.The differential equations of Kelvin viscoelastic cylinder are converted into dimensionless equations with introduction of dimensionless quantities.