Longitudinal hydrodynamic expansion of the fluid created in relativistic heavy-collisions is considered taking into account shear viscosity. Both a on-vanishing viscosity and a soft equation of state make particle distributions in rapidity narrower. The presence of viscosity has dramatic consequence on the value of the initial energy density. The reduction of the longitudinal work and dissipative processes due to the shear viscosity, increase the total entropy and the particle multiplicity at

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... ntral rapidities. The total energy in the collision, dominated by the longitudinal motion, is conserved. Viscous corrections make the longitudinal velocity of the fluid to stay close to the Bjorken scaling v_z = z/t through the evolution. At the freeze-out viscous corrections are the strongest for non-central rapidities.