We report on shear-stress relaxation of melts of poly(butylcarbosilane) dendrimers. The system is studied by means of the molecular dynamics simulations with atomistic resolution. The key investigated quantities are the dynamical shear-stress relaxation modulus and, its counterparts in the frequency domain, the storage and loss moduli. We show the existence of three main characteristic regimes of the mechanical relaxation (going from high to low frequencies): (i) relaxation of tension related to the finite extensibility of the macromolecules; (ii) relaxation related to the dendritic architecture (inner and branch relaxation); and (iii) mobility of the dendrimer as a whole. The tension relaxation is independent of the dendrimers' size and leads to a power law characterized by an exponent 0.7. The processes at low frequencies (branch relaxation and dendrimer mobility as a whole) strongly depend on the molecular mass and do not lead to a universal behavior.