Axially directed blood plasma flow can significantly accelerate thrombolysis of non-occlusive blood clots. Viscous forces caused by shearing of blood play an essential role in this process, in addition to biochemical fibrinolytic reactions. An analytical mathematical model based on the hypothesis that clot dissolution dynamics is proportional to the power of the flowing blood plasma dissipated along the clot is presented. The model assumes cylindrical non-occlusive blood clots with the flow channel in the centre, in which the flow is assumed to be laminar and flow rate constant at all times during dissolution. Effects of sudden constriction on the flow and its impact on the dissolution rate are also considered. The model was verified experimentally by dynamic magnetic resonance (MR) microscopy of artificial blood clots dissolving in an in vitro circulation system, containing plasma with a magnetic resonance imaging contrast agent and recombinant tissue-type plasminogen activator (rt-PA). Sequences of dynamically acquired 3D low resolution MR images of entire clots and 2D high resolution MR images of clots in the axial cross-section were used to evaluate the dissolution model by fitting it to the experimental data. The experimental data fitted well to the model and confirmed our hypothesis.