Inelastic deformation behavior of metals and alloys is considered rate dependent. Uniaxial ratcheting experiments performed by Ruggles and Krempl, and Hassan and Kyriakides exhibited that higher mean stress for a fixed stress amplitude resulted in higher ratchet strain within a rate independent framework and higher stress rate resulted in lower ratchet strain, respectively. These phenomena are qualitatively investigated by numerical experiments through unified viscoplasticity theory. The theory does not separate rate-independent plasticity and rate-dependent creep, and thus uses only one inelastic strain to describe inelastic deformation processes with the concept of the yield surface. The growth law for the kinematic stress, which is a tensor valued state variable of the constitutive equations, is modified to predict the linear evolution of long-term ratchet strain.