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We consider a body which under stress exhibits an elastic, a viscous, and a retarded elastic response. For the particular case of a constant velocity applied at the end of a semi‐infinite bar, the transient stresses, strains and velocities are found by the method of characteristics. From this solution can also be obtained the stresses for the case of a constant stress applied at the end of a semi‐infinite bar. By superposition we can also solve problems involving finite bars. For a constant velocity applied at the end of the bar an integral expression is derived for the stress at that end as a function of time.