A visco-elastohydrodynamic model of a hydraulic rod seal during transient operation has been developed. The model includes analyses of the macro- and microscale deformation mechanics and contact mechanics, and the microscale fluid mechanics. Viscoelasticity enters the analysis through the deformation mechanics and through the contact mechanics. A hybrid finite element-finite volume computational framework is developed to solve the highly coupled governing equations. Viscoelasticity is seen to affect the leakage and friction characteristics of the seal through its effects on the changing fluid pressure and contact pressure distributions as the rod velocity and sealed pressure change during a cycle. Compared with purely elastic behavior, viscoelasticity increases the fluid pressure and the contact pressure significantly in the sealing region closest to the sealed end, shifts the fluid pressure peaks away from the sealed end during the instroke, and enhances the cavitation during the outstroke. It results in thicker fluid films and produces a significant increase in the Poiseuille flow during the instroke.