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\nWe present the open-source software <monospace>RheoVolution</monospace>, a computational implementation of the tidal theory based on the Association Principle, which provides a direct link from the adopted rheological model to the body’s deformation matrix in the time domain, thus facilitating the use of more complex rheological models. The code introduced here simulates the motion of N deformable bodies that remain slightly aspherical at all times. Each body can exhibit permanent triaxiality and possess its own rheology, ranging from a simple Maxwell rheology to complex rheologies equivalent to that of multilayered bodies with viscoelastic homogeneous layers. We showcase our program capabilities by reproducing different dynamical phenomena in the Solar System, namely, Earth’s Chandler wobble and true polar wander, Moon’s orbital drift, and Moon’s stabilization in the Cassini state 2.\n