In this paper we study the three-dimensional response of isotropic viscoelastic solid-like polymers undergoing degradation due to mechanical stimuli. A single integral model is used to describe the time-dependent behaviors of polymers under general loading histories. The degradation is associated to excessive deformations in the polymers as strains continuously increase when the mechanical stimuli are prescribed, and therefore we consider a degradation threshold in terms of strains. The degradation part of the deformations is unrecoverable, and upon removal of the prescribed external stimuli, the accumulation of the degradation strains lead to residual strains. We also systematically present material parameter characterization from available experimental data under various loading histories, i.e., ramp loading with different constant rates, creep–recovery under different stresses, and relaxation under several strains. We analyze viscoelastic-degradation response of two polymers, namely polyethylene and polyoxymethylene under uniaxial tensile tests. Longer duration of loading can lead to increase in the degradation of materials due to the substantial increase in the deformations. The single integral model is capable in predicting the time-dependent responses of the polymers under various loading histories and capturing the recovery and residual strains at different stages of degradations.