An anisotropic-ice flowline model is applied to a flowline through Swiss Camp (69.57° N, 49.28° W), West Greenland, to estimate the dates of internal layers detected by radio-echo sounding measurements. The effect of an anisotropic-ice fabric on ice flow is incorporated into the steady-state flowline model. The stress–strain-rate relationship for anisotropic ice is characterized by an enhancement factor based on the laboratory observations of ice deformation under combined compression and shear stresses. By using present-day data of accumulation rate, surface temperature, surface elevation and ice thickness along the flowline as model inputs, a very close agreement is found between the isochrones generated from the model and the observed internal layers with confirmed dates. The results indicate that this part of the Greenland ice sheet is primarily in steady state.