The methodology in the seismic design of slopes has evolved with technological advancement and the development of geotechnical engineering. Since methods with great limitations such as pseudo-static analysis to rigorous methods that require a lot of information for a better understanding of the behavior of the soil such as the dynamic analysis.  This article develops the procedure, comparison, and application of methods for estimating seismic displacements, which are the Newmark (1965), Sarma (1975), Makdisi & Seed (1978) and Bray, Macedo & Travasarou (2018). Each of these methods considering the criteria of each one to obtain permanent displacements, such as yield acceleration, degraded period, spectral acceleration, magnitude, etc.  As an applicative case, a rockfill dam and core central 50 m high placed in sandstone strata and moraine deposits interspersed with shale...