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Abstract Dislocation‐based dissipation mechanisms potentially control the viscoelastic response of Earth's upper mantle across a variety of geodynamic contexts, including glacial isostatic adjustment, postseismic creep, and seismic‐wave attenuation. However, there is no consensus on which dislocation‐based, microphysical process controls the viscoelastic behavior of the upper mantle. Although both intergranular (plastic anisotropy) and intragranular (backstress) mechanisms have been proposed, there is currently insufficient laboratory data to discriminate between those mechanisms. Here, we present the results of forced‐oscillation experiments in a deformation‐DIA apparatus at confining pressures of 3–7 GPa and temperatures of 298–1370 K. Our experiments tested the viscoelastic response of polycrystalline olivine—the main constituent of the upper mantle—at stress amplitudes from 70 to 2,800 MPa. Mechanical data are complemented by microstructural analyses of grain size, crystallographic preferred orientation, and dislocation density. We observe amplitude‐ and frequency‐dependent attenuation and modulus relaxation and find that numerical solutions of the backstress model match our results well. Therefore, we argue that interactions among dislocations, rather than intergranular processes (e.g., plastic anisotropy or grain boundary sliding), control the viscoelastic behavior of polycrystalline olivine in our experiments. In addition, we present a linearized version of the constitutive equations of the backstress model and extrapolate it to conditions typical of seismic‐wave propagation in the upper mantle. Our extrapolation demonstrates that the backstress model can explain the magnitude of seismic‐wave attenuation in the upper mantle, although some modification is required to explain the weak frequency dependence of attenuation observed in nature and in previous experimental work.