This paper is a presentation of a Finite Element Modeling Software named FEMS that integrates mesh generation and adaption features in order to alleviate significantly the difficulty of designing a Finite Element (FE) mesh for a particular problem. FEMS is targeted at engineers and scientists addressing localization problems in mechanics, although it should be suited to many other applications. FEMS is particularly relevant for problems with internal interfaces, both in solid and fluid mechanics, as it has both explicit and implicit interface representation. The former can be generated from signed distance functions using body-fitted meshing capabilities implemented in FEMS, while the latter relies on the level-set method. The choice between the one or the other can be made by the user depending on the severity of deformations in the neighborhood of an interface. During the simulation, FEMS adapts the FE mesh automatically to achieve the best accuracy for a prescribed number of nodes. This is possible for both linear and quadratic interpolation. Additionally, in an updated Lagrangian setting, FEMS triggers mesh adaption automatically to avoid element flipping during node motion. The capabilities of FEMS are demonstrated in this paper for fluid and solid mechanics problems featuring turbulence, multiphase flow, large deformations and plasticity. This wide range of problems that can be handled by FEMS should prove its great interest for the computational mechanics commmunity.