In this contribution I will describe some objects of the generalized geometry that appear naturally in the qualitative analysis of mechanical systems. In particular we will discuss the Dirac structures within the framework of the systems with constraints and eventually of port-Hamiltonian systems. From the mathematical point of view, Dirac structures generalize simultaneously symplectic and Poisson structures. I will present an approach to variational formulation of dynamics on Dirac structures. As for mechanics, the idea is to design numerical methods that preserve these structures and thus guarantee good physical behaviour in simulations.