Understanding grounding-line dynamics is necessary for predictions of long-term ice-sheetstability. However, despite growing observations of the tidal influence on grounding-line migration, thisshort-timescale migration is poorly understood, with most modeling attempts assuming beam theory tocalculate displacements. Here we present an improved model of tidal grounding-line migration thattreats migration as an elastic fracture problem, forced by the additional ocean water pressure from thetide. This new model predicts that the grounding line cannot be assumed to be in hydrostaticequilibrium and, furthermore, that migration is inherently asymmetric and nonlinear, with migrationdistances that are not proportional to the tidal load. Specifically, for constant surface slope, thegrounding line migrates upstream approximately ten times further as the tide rises from mean sea levelto high tide than it migrates downstream as the tide falls from mean sea level to low tide, and migrationdistances are substantially larger than simple flotation arguments suggest. Numerical tests also showthat the dependence of migration distance on elastic moduli and ice-sheet thickness are inconsistentwith predictions of beam theory for a range of realistic values. Finally, applying the new model toobservations in Antarctica results in new estimates of bed slopes, though these estimates remainuncertain due to imperfect knowledge of the relevant rheological parameters.