Abstract: The geomembranes (GMs) are often used as the first liners in landfills to block the upper leachate and prevent the toxic substances from migrating to the underlying soil layer (SL). However, during the construction or service periods, defects are easily caused in the GMs by external forces, which can greatly reduce their barrier capacity. In view of this, a two-dimensional migration model for the contaminant transporting through a defected GM to the underlying SL is established with time-dependent pollution source. The Laplace transform, Fourier transform and boundary transformation methods are employed to obtain the semi-analytical solution for contaminant concentration. Later, the correctness and reliability of this study are verified by comparing the numerical results and the semi-analytical solutions. The migration characteristics of pollutants in the SL through the defected GM are investigated against different parameters under the temporal and spatial domains. The results indicate that the migration is faster with larger defect rate, and the smaller defect rate leads to the higher sensitivity to concentration variations. In addition, the peak values of concentration exist when the exponential concentration function is adopted, and the higher and later peak is produced with the larger concentration function parameter.