We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a contrast of O(10²) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(10²) and O(104) years. The principal mode is embedded within this continuous spectrum. From this initial‐value approach we have found that for the low degree harmonics the non‐modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time‐domain and normal‐mode results are found to decrease strongly with increasing angular order. These calculations also show that a time‐dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes.