This paper discusses Hamel's formalism for simple hybrid systems and explores the role of reversing symmetries in these system with a continuous-discrete combined dynamics. By extending Hamel's formalism to the class of simple hybrid systems with impulsive effects, we derive, under some conditions, the dynamics of Lagrangian hybrid systems and Hamiltonian hybrid systems. In particular, we derive Euler-Poincare and Lie-Poisson equations for systems with impulsive effects as a simple hybrid system. A reversing symmetry in the phase-space permits one to construct a time reversible hybrid Hamiltonian system. Based on the invariance of a Hamiltonian function by a reversing symmetry, we can find sufficient conditions for the existence of periodic solutions for these simple hybrid systems.