Within the context of seismic wave propagation, fractures can be described as thin layers or linear-slip interfaces. In this paper, numerical simulations of elastic wave propagation in a medium with a single fracture represented by these two models are performed by 2D finite-difference codes: a variable-grid isotropic code for the thin-layer model and a regular-grid anisotropic code for the linear-slip model. Numerical results show excellent agreement between the two models for wavefields away from the fracture; the only discrepancy between the two is the presence of a slow wave traveling primarily within the fracture fluid of the thin-layer model. The comparison of the computational cost shows that modeling of the linear-slip model is more efficient than that of the thin-layer model. This study demonstrates that the linear-slip model is an efficient and accurate modeling approach for the remote seismic characterization of fractures.