We implement a spectral‐element method for 3D time‐independent elastoplastic problems in geomechanics. As a first application, we use the method for slope stability analyses ranging from small to large scales. The implementation employs an element‐by‐element preconditioned conjugate‐gradient solver for efficient storage. The program accommodates material heterogeneity and complex topography. Either simple or complex water table profiles may be used to assess effects of hydrostatic pressure. Both surface loading and pseudostatic seismic loading are implemented. For elastoplastic behavior of slopes to be simulated, a Mohr–Coulomb yield criterion is employed using an initial strain method (i.e., a viscoplastic algorithm). For large‐scale problems, the software is parallelized on the basis of domain decomposition using Message Passing Interface. Strong‐scaling measurements demonstrate that the parallelized software performs efficiently. We validate our spectral‐element results against several other methods and apply the technique to simulate failure of an earthen embankment and a mountain slope.